Step 1: In a medium bowl, combine the cooked chicken with mayonnaise (or Greek yogurt), lime juice, salt, and pepper. If desired, stir in finely diced jalapeños and/or hot sauce. Mix until the chicken is thoroughly coated.
Step 2: Lay out the bread slices on a clean surface. Spread half of the chicken mixture evenly onto one slice of bread. Layer half of the sliced avocado over the chicken, then generously sprinkle with half of the shredded cheese. Top with a second slice of bread.
Step 3: Repeat the layering for the second sandwich. Heat a skillet or panini press over medium heat. If using a skillet, lightly butter or brush with olive oil.
Step 4: Place the assembled sandwiches onto the heated surface. Cook for approximately 3-4 minutes per side, or until the bread is golden brown and crispy, and the cheese is completely melted and bubbly. Press gently with a spatula for even browning.
Step 5: Carefully remove the hot sandwiches from the pan. Slice each diagonally in half to reveal the irresistible, gooey interior. Serve immediately and enjoy your ultimate chicken avocado melt!