In a small bowl, combine butter, garlic, and chile flakes. In a medium bowl, whisk egg and milk. Spread parmesan on a plate.
In a large frying pan, melt half the seasoned butter over medium heat. Dip 1 bread slice in egg mixture, coating one side only. Dip coated side into parmesan. Place to one side in frying pan, cheese side down. Repeat with 1 of remaining bread slices. Arrange turkey, avocado, cilantro, and muenster on slices, dividing evenly.
Dip remaining bread into egg and then into parmesan. Arrange on sandwiches, cheese side up, and cook over medium heat until undersides are golden brown, 3 to 4 minutes. Lift sandwiches and add remaining butter to pan; flip and cook until second side is golden brown, 3 to 4 minutes more.
Note: Nutritional analysis is per sandwich.