Gather all ingredients and equipment to create an efficient cooking process., Cook the chicken if not already done, whether by boiling, grilling, or roasting, and shred or slice it into bite-sized pieces., Cut the avocado in half, remove the pit, and scoop the flesh into a mixing bowl., If using raw chicken, season with salt and pepper. Place in boiling water or grill until cooked through, about 15-20 minutes., Once cooked, allow the chicken to cool slightly, then shred or slice it into pieces for the sandwich., In the mixing bowl with the avocado, add mayonnaise, lime juice, salt, and pepper., Mash the mixture with a fork until you reach a spreadable consistency, leaving some chunks for texture. Taste and adjust seasoning as needed., Lay one slice of the bread on the cutting board and spread a generous amount of the avocado mixture., Layer the shredded or sliced chicken on top of the avocado., Sprinkle the cheese generously over the chicken., Optionally add fresh greens and tomato slices before placing the second slice of bread on top., Preheat the skillet over medium heat and add a touch of oil or butter to prevent sticking., Place the sandwich carefully onto the skillet; cook until the bottom slice is golden brown, about 3-4 minutes., Flip the sandwich gently using the spatula, and cook the other side until the cheese melts and the bread is golden, about another 3-4 minutes.