In a medium bowl, mix together the tuna, mayonnaise, pickled jalapeños, smoked paprika, garlic powder, onion powder, cayenne, and a pinch of salt and pepper. Taste and adjust the seasoning—add more jalapeños or cayenne if you want extra heat. Use a fork to mash the tuna so there are no large chunks.

Lay out 4 slices of sourdough. Add 1 slice of sharp Cheddar to each, then divide the tuna mixture evenly over the cheese. Top with the remaining 4 slices of Cheddar and finish with the last 4 slices of bread.

Heat a large skillet over medium heat for about 3 minutes, until hot. Spread a thin layer of softened butter on the top slice of each sandwich, then place them butter-side down in the skillet. Cook for 4–6 minutes, or until the bottoms are golden and crispy. Cook in batches if needed to avoid overcrowding.

While the first side cooks, butter the top of each sandwich. Flip carefully and cook for another 2–3 minutes, until the second side is golden and crisp.

Transfer the sandwiches to a cutting board, slice, and serve warm.