Start by preheating your oven to 400°F. While that's heating, grab a small bowl and combine your olive oil, red wine vinegar, stone-ground mustard, garlic powder, salt, and fresh cracked pepper. Whisk these together until they're well combined—you want the mustard fully incorporated and the mixture to look slightly emulsified. This vinaigrette is the flavor foundation of the entire dish, so don't skip this step or rush it. A thorough whisking takes maybe 90 seconds and makes a noticeable difference.

Rinse your bell peppers and onion under cool running water. Slice each pepper in half lengthwise, remove the seeds and white membrane (this is where bitterness lives), and slice them into ¼-inch strips. For your onion, slice it in half root-to-tip, peel away the papery skin, and slice those halves into ¼-inch strips as well. The consistent thickness matters—¼-inch strips cook evenly and caramelize beautifully. Thicker pieces won't soften properly in 40 minutes; thinner pieces might get too soft and lose their texture.

Spread your sliced peppers and onions across a large rimmed baking sheet in a relatively even layer (they don't have to be perfectly organized, but try not to create huge piles where vegetables stack on top of each other). Place your five bratwurst links directly on top of the vegetables, spacing them out so heat can circulate around each one. Pour your prepared vinaigrette evenly over everything—don't hold back here, it looks like more than enough but it's perfect. Now comes the important part: toss everything together with a pair of tongs or two large spoons until every piece of vegetable and each bratwurst is coated in vinaigrette. You want oil glistening on everything. This distributes the flavor evenly and ensures nothing sticks to the pan.

Place your sheet pan in the preheated 400°F oven. Set a timer for 20 minutes. You're not checking it during this time—the oven does its work undisturbed. After 20 minutes, carefully pull the pan out and give everything a thorough stir. You want to flip the bratwurst to the other side and redistribute the vegetables so they cook evenly. At this point, you'll notice the peppers and onions have started to soften and the bratwurst is beginning to brown.

Return the sheet pan to the oven for another 20 to 25 minutes. You're looking for the vegetables to become tender with deep golden-brown edges and the bratwurst to be cooked through with browned skin. The longer you roast in this final phase, the more caramelization you get—which means more complex flavor. If you like your vegetables with more char, go the full 25 minutes. If you prefer them softer but less browned, 20 minutes is fine.

If you're adding cheese topping, sprinkle the shredded cheddar over your hot vegetables and bratwurst right out of the oven. Place the sheet pan back in the 400°F oven for about 5 minutes to let the cheese melt completely. While that's happening, lay your buns out on another sheet pan or directly on the oven rack. Toast them for 2 to 3 minutes until they're warm and lightly golden. Pull both pans out simultaneously—you want everything warm and ready to assemble.

Place one bratwurst link into each warm bun, top with a generous handful of the roasted peppers and onions, and drizzle with prepared mustard if desired. Serve immediately while everything is still warm. The contrast of warm sausage, tender vegetables, and crusty bread creates an incredibly satisfying meal.