In a large, heavy saucepan, heat 1 tbsp. oil over medium heat. Add onion; sauté until golden, 5 minutes. Stir in celery and carrot; cook 5 more minutes. Add sausage and 1/2 tsp. salt, breaking up meat with a spoon, and cook until it loses its raw color.
Add milk and cook over medium heat, stirring, until completely evaporated, 10 to 12 minutes. (The mixture will appear quite curdled at this point.) Add wine and cook until reduced by half, about 3 minutes. Add tomatoes and juice, bring to a boil, lower heat, and gently simmer, uncovered. Cook ragù until liquid reduces by a third, about 30 minutes. Season with 1/4 tsp. pepper and remaining 1/2 tsp. salt.
In a food processor, whirl cottage cheese, egg, 1/4 cup parmesan, remaining 1/4 tsp. pepper, and the nutmeg until smooth.
Preheat oven to 375°. Cook lasagna noodles according to package directions; don't overcook. Drain noodles and lay flat on kitchen towels without overlapping. Oil a 9- by 13-in. baking dish and spread with about 1/2 cup ragù. Add a single layer of noodles (for most brands this is 3 sheets per layer). Spread with a third of ragu, then top with another layer of noodles, half the cheese mixture, and another layer of noodles. Repeat layering, giving you 2 alternating layers of sauce and cheese. Cover with remaining third of ragù and sprinkle evenly with remaining parmesan.
Cover lasagna with oiled foil and bake until hot, 30 minutes. Let stand 15 minutes before serving.
Note: Nutritional analysis is per serving.