01 - In a skillet over medium heat, melt 1 tablespoon of unsalted butter. Add the thinly sliced apple, brown sugar, ground cinnamon, and a pinch of salt. Sauté for 4 to 5 minutes, stirring occasionally, until the apples are tender and caramelized. Remove from heat and set aside.
02 - Butter one side of each slice of bread. Place two slices, buttered side down, on a clean work surface.
03 - On each prepared bread slice, layer with 2 slices of sharp cheddar cheese, half of the caramelized apples, and 1 slice of mozzarella cheese. Top with the remaining bread slices, ensuring the buttered sides face upwards.
04 - Heat a nonstick skillet or griddle over medium-low heat. Carefully place the assembled sandwiches in the pan. Cook for 3 to 4 minutes per side, pressing gently with a spatula, until the bread is golden brown and the cheese is fully melted.
05 - Remove the grilled sandwiches from the pan. Allow them to cool slightly before slicing and serving warm.