In a medium mixing bowl, whisk together the mayonnaise, minced chipotle peppers, lime juice, garlic powder, and salt until a smooth emulsion is formed.

Fold the shredded chicken into the chipotle mayonnaise mixture until all pieces are evenly coated.

Apply the softened butter to one side of each sourdough bread slice, ensuring edge-to-edge coverage for optimal browning.

On the non-buttered side of two slices, layer 1/4 cup of shredded cheese followed by a generous portion of the chicken mixture.

Arrange the avocado slices over the chicken and top with the remaining shredded cheese to act as a binding agent.

Place the remaining bread slices on top with the buttered side facing outward.

Heat a non-stick skillet or cast-iron griddle over medium heat until the surface reaches approximately 350°F (175°C).

Place the sandwiches in the skillet and grill for 3 to 4 minutes per side, applying light pressure with a spatula to ensure even heat distribution.

Remove from heat once the bread is golden brown and the internal cheese is fully melted.

Allow the sandwiches to rest for 60 seconds to set the filling before slicing diagonally for service.