1) Make the crespelle: Blend together the eggs, water, flour, and salt in a blender or food processor until smooth.
2) Cover and let stand for 30 minutes.
3) Check the batter consistency; it should be lighter than pancake batter. If it seems thicker, whisk in 1 tablespoon water.
4) Lightly brush a 7 3/4" crêpe pan with melted butter and heat over moderate heat until hot but not smoking.
5) Ladle about 1/4 cup batter into the pan, tilting and rotating it to coat the bottom.
6) Cook until the bottom of the crespella is barely golden, about 30 seconds to 1 minute.
7) Flip and cook until the bottom is set, about 30 seconds.
8) Transfer cooked crespelle to a rack to cool. (You can stack them as soon as they have cooled). You should have enough batter to make 6 crespelle.
9) Make the filling: Preheat the oven to 375°F.
10) Brush both sides of the eggplant slices with oil and sprinkle with salt and pepper.
11) Arrange in one layer on a large sheet pan lined with parchment.
12) Bake until tender and starting to color, about 40 minutes.
13) Remove from the oven, gently loosen from the pan, and let cool.
14) Combine the cheeses and season lightly with salt and pepper.
15) Top each of the crespella with 2 to 3 eggplant slices (or 1/6 of the eggplant).
16) Spread 1/6 of the cheese mixture just inside the edge of the crespella closest to you.
17) Roll up each crespella to enclose the cheese and eggplant, and arrange it seam-side down in a gratin or shallow casserole dish.
18) Pour the tomato sauce over all the crespelle. Top with additional grated Parmesan cheese, if desired.
19) Bake until the sauce is bubbly and the cheese is melted, about 30 minutes.
20) For appetizer servings, transfer 1 stuffed crespella to each plate and top with some of the fresh basil.