Prepare the Chipotle Sauce:
To make the chipotle sauce whisk together the mayonnaise, adobo sauce, minced garlic, lime juice, salt, and black pepper in a small bowl. Adjust the seasoning to your liking. Set aside.
Heat a griddle or large skillet over medium heat.
Spread a generous layer of the chipotle sauce on one side of each slice of bread.
Add a layer of shredded cheese onto 3 slices of bread.
Place smoked chicken slices evenly over the cheese.
Top the chicken with sliced avocado, then add another layer of cheese.
Cover with the remaining bread slices, sauce-side down.
Melt 1 tablespoon of butter on the preheated skillet. Place one sandwich onto the skillet. Repeat with the other sandwiches if your skillet has room.
Cook for 2-3 minutes or until the bread is golden and crispy.
Carefully lift the sandwich, add another small pat of butter to the pan, and flip the sandwich to grill the other side.
For extra melty cheese, cover the sandwiches with a piece of aluminum foil while cooking.
Remove the sandwiches from the skillet, cut them in half (if desired), and serve hot. Pair with a side salad or some tortilla chips for a complete meal!