Combine grapes, sugar, vinegar, mustard seeds, Aleppo pepper, and salt in a medium saucepan over medium. Bring to a boil, stirring often. Reduce heat to medium-low, and cook, stirring often, until mixture reduces to the consistency of loose jam, about 30 minutes. Remove from heat, and let cool completely, about 30 minutes.
Spread 2 bread slices with 1/2 tablespoon mostarda each. Top each with 1 slice of cheddar, 1/2 ounce crumbled blue cheese, and 2 slices prosciutto. Spread remaining 2 bread slices with 1/2 tablespoon mostarda each. Place bread slices, mostarda side down, over prosciutto. Spread butter evenly on both sides of sandwiches.
Heat a large nonstick skillet over medium. Add sandwiches to skillet; lightly cover with aluminum foil, and place a large cast-iron skillet on top to compress. (Alternatively, use a heavy skillet weighted with 2 heavy cans.) Cook, flipping sandwiches once and adjusting heat as necessary, until bread is golden brown and toasted and cheese melts, about 2 minutes per side. Serve immediately with remaining mostarda on the side.
