Preheat grill to medium-high heat.
To make the vegetables, heat oil in a nonstick skillet over medium-high heat. Once hot, sauté peppers and onion for 5 minutes, until softened. Season with salt and pepper.
Add beer and cook, covered, for 8 to 10 minutes, until almost caramelized. Remove from heat and set aside.
Place bratwurst on the grill and cook for 10 to 15 minutes, turning frequently for even cooking. Once fully cooked (145˚F to 150˚F internally), removed from grill.
While the brats are grilling, melt butter for the cheese sauce in a small saucepan over medium heat. Once melted, whisk in flour and garlic powder, cooking for an additional minute while stirring constantly.
Slowly whisk in milk. Cook, stirring frequently, until it comes to a light boil and thickens.
Reduce heat to low and stir in cheese. Cook until cheese is melted, stirring constantly, about 3 to 4 minutes. Season with salt and pepepr to taste. If too thick, you can thin it out by adding a little milk.
Place cooked brats in buns, then top with beer braised vegetables and cheese sauce. Serve immediately.