Mix together the honey and vinegar in a small bowl and stir in the strawberries; set aside for the berries to macerate while you make the sandwiches. Spread 1 teaspoon butter on 1 side of each slice of bread. Place 1 slice of bread (butter side down) on a cutting board; top each with 1 1/2 tablespoons strawberry preserves and 1 1/2 pieces of cheese. Place the remaining slice of bread on top (butter side up). Grill the sandwiches in a large skillet (or on a griddle) over low heat until golden on both sides. To serve, transfer each sandwich to a plate and sprinkle on a dusting of powdered sugar if desired. Serve the sandwiches hot along with the macerated strawberries to spoon on top.