Position an oven rack 4 inches from the broiler element and preheat to high.
Place whole jalapenos on a baking sheet and broil for 5 to 7 minutes, turning occasionally until skin is charred and blistered.
Transfer charred peppers to a bowl, cover with plastic wrap, and let steam for 5 minutes. Peel away skins, remove stems and seeds, and slice into thin strips.
In a small mixing bowl, combine cream cheese, garlic powder, and smoked paprika until smooth.
Apply the cream cheese mixture evenly to one side of each slice of bread.
On two of the slices, layer half of the cheddar cheese, the roasted jalapeno strips, crumbled bacon, and the remaining cheddar cheese.
Place the remaining bread slices on top, cream cheese side down, to close the sandwiches.
Spread butter onto the exterior surfaces of the sandwiches.
Heat a heavy-bottomed skillet over medium heat. Grill sandwiches for 3 to 4 minutes per side until the bread is golden brown and the cheese core is fully melted.
Let stand for 1 minute before slicing diagonally.