Spread 1/2 tablespoon butter onto one side of each slice of bread to cover evenly. With buttered sides of the bread facing out, layer 1 slice American cheese, 2 slices tomato, and 2 slices avocado onto each of 2 of the bread slices.
Sprinkle about half the basil, red pepper flakes, and garlic salt atop the avocado layer. Finish by topping each with half the mozzarella and 1 slice provolone. Top each with 1 of the remaining bread slices with the buttered side facing out.
Cook in hot skillet until bread is golden brown and cheese is melted, 3 to 4 minutes per side.