To roast the bell pepper and jalapeño, cut the bell pepper in half. Place the halves along with the whole jalapeno on top of a piece of foil (turn the sides up to contain any juices) on top of a baking sheet. Broil, turning and adjusting as needed, until blistered and lightly charred in places. Remove from oven as each piece is ready.

If the foil is large enough, simply fold it over the peppers and tightly seal; it not, place in a medium bowl and cover with plastic wrap; let steam 10 minutes. Peel and seed peppers, then finely chop.

Mix mayonnaise, garlic powder, cayenne, and paprika in a medium bowl. Fold in cheddar and chopped peppers; season with salt and black pepper to taste.