Heat the broiler to high with a rack no more than 6 inches from the heat source. Line a sheet pan with foil. Add the jalapeños, cut side down. Broil until blackened and flattened, about 6 to 8 minutes, rotating the pan halfway through. Transfer the jalapeños to a bowl and cover tightly with foil to steam. Peel away and discard the skins.

If using bacon, add it to a skillet over medium heat and cook for about 8 minutes, flipping halfway through, until crispy. Transfer bacon to a plate and pour the fat into a heatproof jar. (Skip this step if using potato chips.)

Lay 2 slices of bread on a work surface. Top each with a slice of cheese, 4 jalapeño halves, half the bacon or potato chips, another slice of cheese, and the remaining slice of bread.

Generously smear both sides of each sandwich with butter and sprinkle with garlic powder.

Heat the skillet over medium heat. Add the sandwiches and cook until crispy on both sides and melty in the middle, about 5 to 8 minutes total. Lower the heat if the sandwiches are browning too quickly, and add a little butter if the pan looks too dry.

Cut in half, sprinkle with salt if desired, and serve immediately.