Make the meatballs: Mix the sausage and parsley in a bowl with your hands until combined. Dampen your hands and form the meat into 3/4-inch balls (you should have about 40). Heat the olive oil in a large pot over high heat. Working in batches, add the meatballs and cook, turning, until browned, about 7 minutes. Transfer to a plate using a slotted spoon.
Reduce the heat to medium high and add the soppressata, onion, celery, carrots and garlic. Cook, stirring occasionally, until the vegetables are slightly softened, about 6 minutes. Add the tomato paste and basil and cook, stirring, 3 minutes. Stir in the wine, tomato puree and 3 cups water. Reduce the heat to medium low and return the meatballs to the pot. Simmer, stirring occasionally, until the sauce thickens, 1 hour, 20 minutes.
Prepare the lasagna: Whisk the ricotta, eggs and parmesan in a medium bowl. Fill a large bowl with hot water. Working in batches, soak the noodles until just pliable, about 5 minutes. Lay out on a clean kitchen towel and pat dry.
Preheat the oven to 400 degrees F. Butter the bottom and sides of a deep 10-by-13-inch baking dish. Lay 6 noodles in the bottom of the dish so they go partway up the sides and overlap slightly. Spread half of the ricotta mixture over the noodles, then top with half of the meatballs and 1 1/2 cups sauce. Sprinkle with half each of the mozzarella and pecorino. Repeat the layers (noodles, ricotta mixture, meatballs, sauce, mozzarella and pecorino). Top with the remaining 6 noodles and cover with the remaining sauce.
Tightly cover the dish with foil and bake until bubbly, about 30 minutes. Uncover and bake until browned, about 15 more minutes. Let stand 20 minutes before serving.