In a large mixing bowl, combine the shredded chicken, salt, ground black pepper, crushed red pepper flakes, chipotle sauce, Greek yogurt, chopped chives, diced red onion, grated carrot, and cheddar cheese. Stir until all ingredients are well mixed.

Spread a generous layer of butter on one side of each slice of thick-cut sandwich bread. Preheat a skillet over medium heat, then place the buttered slices butter-side down in the skillet. Toast them for 2–3 minutes until golden brown.

Flip the toasted bread slices so the non-buttered sides are facing up. Spread the chicken filling over the toasted side of one slice. Top with mozzarella cheese, then place another slice of bread on top, buttered side facing up.

Carefully place the assembled sandwich back in the skillet over medium-low heat. Spread a thin layer of butter on the outer side of the top slice. Grill for 3–4 minutes until the bottom is golden and crispy, then flip the sandwich and grill the other side.

Once both sides are golden and the cheese is melted, remove it from the skillet, let it cool for a minute, then slice diagonally and serve warm.