Preparation Arrange 4 bread slices on work surface. Layer each with 1/4 cup mozzarella cheese, 2 tablespoons peppers, 1 teaspoon thyme, 2 tablespoons Parmesan cheese, 1 tablespoon goat cheese, and 1 ham slice. Top each with bread slice. Melt 1 tablespoon butter in heavy large skillet over medium-low heat. Add 2 sandwiches to skillet. Cover and cook until bottoms of bread are golden and cheeses are melted, about 2 minutes. Add 1 tablespoon butter to skillet. Turn sandwiches over; cook until bottoms are golden, about 2 minutes longer. Transfer sandwiches to plates. Repeat with remaining butter and sandwiches.
Preparation Arrange 4 bread slices on work surface. Layer each with 1/4 cup mozzarella cheese, 2 tablespoons peppers, 1 teaspoon thyme, 2 tablespoons Parmesan cheese, 1 tablespoon goat cheese, and 1 ham slice. Top each with bread slice. Melt 1 tablespoon butter in heavy large skillet over medium-low heat. Add 2 sandwiches to skillet. Cover and cook until bottoms of bread are golden and cheeses are melted, about 2 minutes. Add 1 tablespoon butter to skillet. Turn sandwiches over; cook until bottoms are golden, about 2 minutes longer. Transfer sandwiches to plates. Repeat with remaining butter and sandwiches.