Place tuna into a mixing bowl and lightly break apart with a fork. Add green onion, celery, capers, chile paste, and mayonnaise. Pinch small pieces from mozzarella cheese into the tuna salad and stir to mix. Season with salt and black pepper; refrigerate tuna salad until needed. Watch Now Heat oven's broiler. Line a baking sheet with aluminum foil. Watch Now Spread butter generously on both sides of French bread slices. Watch Now Broil buttered bread until golden brown on top, 2 to 3 minutes. Flip bread slices and broil other side until toasted, 2 to 3 more minutes. Remove from oven and turn bread slices over on the baking sheet so the darkest sides are on the bottom. Watch Now Gently spread tuna salad onto bread slices using 2 forks. Press the salad onto the bread and spread tuna all the way to the edges of the bread. Spread shredded sharp Cheddar over each sandwich. Dust tops with cayenne pepper. Watch Now Place sandwiches under broiler and cook until cheese is melted and bubbling, 5 to 6 minutes. Watch Now