Preheat oven to 350° F.
Drizzle 1 Tablespoon of olive oil in a cast iron skillet. Heat to medium-high, then add brats and sear for 5 minutes, turning as needed to brown all sides.
Add sliced peppers and onions to the skillet with the brats; season with salt & pepper. Reduce heat to medium and slowly add the beer. Cover and cook for 20 minutes, stirring the vegetables occasionally.
Remove brats from the skillet and slice into pieces (about 8 pieces per brat.) Drain any remaining liquid from the pepper & onion mixture.
Cut the buns in half, being careful to leave them attached if possible. Place the bottom bun halves on a rimmed baking sheet or 9x13 inch pan lined with foil. Brush with mayo and mustard, then layer with brats, vegetables, and cheese. Add the bun tops to complete the sandwiches.
In a small saucepan, melt the butter for the sauce over medium-low heat. Add the remaining ingredients and stir to combine.
Brush the butter sauce over the tops of the buns.
Bake, uncovered, for 15 minutes or until cheese is fully melted.