In a food processor, combine the basil, parsley, mint, Parmesan, pine nuts, anchovy paste, pepper and garlic. Pulse until chunky. With the machine running, gradually add the olive oil until the pesto is smooth.
In a medium bowl, mix together the ricotta, mozzarella, mascarpone, Parmesan, breadcrumbs, nutmeg, 3/4 teaspoon salt and the pepper.
In a small bowl, mix together the egg and 1 teaspoon water until smooth.
Using a pastry brush, lightly brush the edges of the wonton wrappers with the egg mixture. Spoon 1 level tablespoon of the filling into the center of each wonton wrapper. Fold the opposite corners of each wonton wrapper over to form triangle shapes. Seal the edges firmly, pressing out any air around the filling. (Can be made a few hours in advance. Cover with foil and refrigerate until ready to use.)
Bring a large pot of water to a boil over high heat. Add the remaining 1 1/2 tablespoons salt and the olive oil. In batches, add the ravioli to the water and cook, stirring occasionally, until tender but still firm to the bite, about 3 minutes. Using a slotted spoon, carefully remove the ravioli and drain in a colander. Transfer the ravioli to shallow soup bowls. Spoon the sauce over the ravioli and serve.