In a medium bowl, combine the shredded chicken with BBQ sauce, mixing thoroughly until the chicken is well coated.

Preheat a non-stick skillet over medium heat and add 1 tablespoon of butter, allowing it to melt and bubble.

On a slice of your chosen bread, generously spread half of the BBQ chicken mixture. Add a layer of mozzarella cheese, and sprinkle some cheddar for extra flavor.

Carefully place the sandwich into the preheated skillet. Cook for about 3-4 minutes or until the bottom slice is golden brown.

Gently flip the sandwich using a spatula, adding another tablespoon of butter. Grill for an additional 3-4 minutes.

Once both sides are crispy, remove from the skillet, allow to cool, slice in half, and serve hot.