In a large bowl, combine eggs, milk, water, flour, melted butter, and salt. Whisk until smooth and let the batter rest for 30 minutes. Heat a greased non-stick skillet and pour a ladle of batter, swirling to coat evenly, then cook until lightly golden and flip.
Melt butter in a saucepan over medium heat, then whisk in flour to form a paste. Gradually add milk, stirring constantly until thickened, and season with salt and pepper. Set aside to cool slightly.
Pat the shrimp and scallops dry. Sauté shallots in olive oil until soft, then add shrimp and scallops. Cook until opaque and tender, then mix in mushrooms, parsley, and a splash of white wine if using. Season with salt and pepper.
Spoon the seafood mixture onto each crepe, roll or fold them, and place in a baking dish. Pour béchamel sauce over the top and sprinkle with Gruyère cheese. Bake at 375°F (190°C) for 15-20 minutes until bubbly and golden.