1. Combine butter, garlic, and chile flakes in a small bowl. Whisk egg and milk in a medium bowl. Spread Parmesan on a plate.
2. Melt half the garlic butter in a large frying pan over medium heat. Dip 1 bread slice in egg mixture, coating one side only. Dip coated side into Parmesan. Put in frying pan, cheese side down. Repeat with 1 more bread slice. Arrange turkey, avocado, cilantro and Muenster evenly on both slices.
3. Dip remaining 2 bread slices into egg on one side and then into Parmesan. Set on sandwiches in pan, cheese side up. Continue cooking sandwiches over medium heat until undersides are golden brown, 3 to 4 minutes. Lift sandwiches and add remaining garlic butter to pan; flip and cook until second side is golden brown, 3 to 4 minutes.
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