2 tablespoons strawberry preserves (such as Tiptree Little Scarlet)
2 teaspoon drained capers
Unsalted butter, softened
4 (4- x 2 3/4- x 1/2-inch) slices seeded sourdough rye bread (such as Zabar's)
¼ pound Taleggio cheese, rind removed, cut into 1/8-inch-thick slices, divided
1 ½ ounces aged Gruyère cheese, grated (about 1/2 cup), divided
Heat a 10-inch cast-iron skillet over medium. Stir together preserves and capers in a small bowl, lightly smashing capers. Spread butter on one side of each bread slice, and place slices, buttered sides down, on a work surface. Top 2 bread slices evenly with Taleggio slices. Top remaining 2 bread slices with preserves mixture, and top evenly with grated Gruyère. Close sandwiches, buttered sides out, pressing to flatten.
Cook sandwiches in hot skillet until bread is golden on the outside and cheese is melted, about 3 minutes per side. Transfer sandwiches to plates; serve immediately.