Preheat a skillet over medium heat. Butter one side of each piece of bread. Create sandwiches by placing 1 slice of bread, buttered side down, in the skillet. Carefully spread 1 teaspoon of mayonnaise on the bread, then layer the turkey, avocado slices, bacon, and cheddar cheese. Top with another slice of bread. When the bottom is toasted, carefully flip sandwich over to brown the other side of the sandwich.