For the Bechamel Sauce, melt butter in a saucepan over medium heat. Whisk in flour and cook for 1-2 minutes until golden. Gradually whisk in milk, continuing to stir until the sauce thickens. Season with salt, pepper, and nutmeg.
Heat a non-stick skillet over medium heat. Pour about ¼ cup of crepe batter into the skillet, swirling to coat the bottom evenly. Cook for 1-2 minutes until the edges lift, then flip and cook for another minute. Repeat with remaining batter.
To assemble, place a spoonful of the seafood mixture on each crepe, sprinkle with mozzarella cheese, and roll up. Place the filled crepes in a baking dish, pour Bechamel sauce over the top, and sprinkle with parsley.
Bake in a preheated oven at 350°F for 15-20 minutes until heated through and bubbly.