Finely dice your yellow onion into pieces about the size of a lentil. This matters more than you'd think. When onions are cut smaller, they soften faster and distribute their flavor throughout the dish more evenly. Plus, dicing takes maybe three minutes, and doing it before you start cooking means you won't be scrambling once the ground beef hits the pan. Grab your largest, deepest skillet—you'll need it. Have your olive oil measured and ready. This is the moment to set yourself up for success, not to start searching for ingredients while something's burning.

Add 1 tablespoon of olive oil to your skillet over medium heat. Once it's warm and shimmers slightly (this takes about one minute), add your ½ pound of ground beef and your diced onion at the same time. This is important: you're not cooking these separately. The onion's moisture helps the meat cook gently, and the meat's fat helps the onion soften and caramelize. Break the ground beef into small pieces as it cooks—use a wooden spoon or spatula and keep stirring every 30 seconds or so. You're looking for the beef to lose its pink color completely and for the onion to become soft and translucent, which usually takes about 5 to 7 minutes depending on your heat level. The mixture should smell savory and appetizing, not burnt. If the bottom of the pan seems to be browning too aggressively, turn your heat down to medium-low. Once the beef is fully cooked and the onion is soft, take a moment to drain off any excess fat if it looks like there's a pool of grease sitting on top. You want some fat—it carries flavor—but you don't want so much that the final dish feels greasy. Tilt the skillet and blot the top of the meat mixture with a paper towel if needed.

This is the critical moment that makes everything work. Add 2 tablespoons of all-purpose flour directly to the cooked beef and onion mixture. Start stirring immediately and don't stop for one full minute. What you're doing is coating the meat and vegetables with flour, which is absorbing the fat and starting to cook. You'll see the bottom of the skillet start to look lighter as the flour absorbs everything, and it might even look a bit dry. This is exactly right. The flour should smell slightly nutty and toasted—similar to the smell of warm cookies baking. If it smells acrid or burnt, you've gone too far, and you'll need to start over with fresh ingredients. (This is rare, but it happens if your heat is too high.) After one minute of constant stirring, you've created what's called a roux, and this is your thickening agent for the entire dish. Everything you add from here on will thicken beautifully because this flour base is ready to do its job.

Now add your 8-ounce can of tomato sauce and your 2 cups of beef broth. The moment the liquid hits the pan, you'll see the roux start to dissolve and the whole mixture will look thin again. This is completely normal. Keep stirring for about two minutes until the flour is completely distributed throughout the liquid and there are no visible lumps on the bottom of the skillet. This stirring motion is doing the work of thickening. The flour particles are suspending throughout the liquid, and as the mixture heats, it'll thicken into a proper sauce. Taste the mixture now and add a pinch of salt and pepper—remember that your broth is already salted, so go easy. You're looking for it to taste like a savory beef broth with tomato notes, nothing fancy.

Add your ½ pound of uncooked pasta shells directly to the liquid. Stir everything together so the pasta is as submerged as possible. Don't worry if some pasta is peeking out of the liquid—it'll cook in steam and will fully submerge as the pasta absorbs liquid. Now turn your heat up to medium-high. You're waiting for the liquid to reach a boil, which usually takes 3 to 5 minutes depending on your stove. You'll see it start to bubble around the edges first, and then larger bubbles will break across the whole surface. That's your signal to proceed to the next step.

Once you reach a boil, give the pasta mixture one quick stir to loosen any pieces that might be stuck to the bottom. Then place a lid on your skillet (even a baking sheet works if you don't have a fitted lid), turn your heat down to low, and set a timer for 10 minutes. The covered skillet does something magical: it traps steam inside, which means the liquid cooks the pasta gently and the sauce doesn't evaporate. The low heat means everything cooks evenly without the bottom burning. You're essentially creating a mini oven in that skillet. After 10 minutes, lift the lid and check your pasta. The pasta should be tender but still have a slight firmness when you bite it, and the sauce should look thick enough to coat the back of a spoon. If the pasta still seems very al dente (very firm), cover it again and give it another 2 to 3 minutes. If the sauce looks too thin, leave it uncovered for a minute or two and let some liquid evaporate. My general rule: if you can bend the pasta without it breaking, it's done. If you need a lot of pressure to bend it, it needs more time.

Once the pasta is tender and the sauce has thickened, turn off the heat. Pour in your 4 ounces of shredded cheddar cheese and stir constantly until every strand of cheese has melted into the sauce. This takes about 2 minutes. The residual heat in the skillet is perfect for melting cheese without it getting scorched. Now add your 2 tablespoons of relish and stir everything together until it's completely incorporated. The relish adds a bright, tangy sweetness that's the secret reason people ask for this recipe. It tastes like a cheeseburger because relish is a classic burger condiment—you're not trying to hide it, you're celebrating it.

Divide the pasta into bowls or plates while it's still hot. Top with sliced green onions if you're using them—they add a fresh bite that contrasts beautifully with the rich, cheesy pasta. Serve immediately. This dish is best enjoyed hot, and if it sits for 20 minutes, it'll start to thicken up as it cools.