Ingredients

5 tablespoons extra-virgin olive oil 

1 pound cremini mushrooms, chopped (about 5 cups) 

1 pound eggplant (1 to 2 medium), peeled and chopped (about 5 cups) 

1 medium onion, chopped (1 1/2 cups) 

2 carrots, peeled and chopped (3/4 cup) 

2 celery stalks, chopped (3/4 cup) 

Kosher salt 

6 garlic cloves, minced (2 tablespoons) 

2 teaspoons dried oregano 

1/2 teaspoon red-pepper flakes 

3 tablespoons tomato paste 

2 cans (28 ounces each) whole peeled tomatoes in juice 

24 ounces whole-milk ricotta (3 cups) 

1 cup whole milk 

3 large eggs 

4 ounces Parmigiano-Reggiano, finely grated (1 1/4 cups) 

1 pound low-moisture mozzarella, shredded (4 cups) 

3/4 cup chopped flat-leaf parsley 

Kosher salt and freshly ground pepper 

18 dry lasagna noodles

Preparation

Preheat oven to 375 degrees.

Sauce: Heat oil in a large saucepan over medium-high. Add mushrooms and eggplant and saute 10 minutes. Add onion, carrots, celery, and 1 teaspoon salt; cook until vegetables have browned in places and most of moisture is cooked out of mushrooms and eggplant, about 15 minutes. Add garlic, oregano, and red-pepper flakes; cook until fragrant, 1 minute. Add tomato paste; cook 2 minutes more. Puree tomatoes in a blender or food processor; add to pan. Bring to a boil, then reduce heat to low and simmer, stirring occasionally, until reduced and thickened slightly but still very loose, about 15 minutes. Remove from heat.

Cheese Mixture: In a large bowl, whisk together ricotta, milk, eggs, 1 cup Parmigiano-Reggiano, 2 1/2 cups mozzarella, parsley, 1 teaspoon salt, and 1/4 teaspoon pepper.

Assembly: Spread 2 cups sauce evenly in a 9-by-13-inch baking dish, preferably ceramic or enameled cast iron. Arrange 3 lasagna noodles over sauce (space noodles evenly; they will expand as the lasagna cooks). Spread 2 cups cheese mixture over noodles; top with 3 more noodles. Repeat layering of vegetable and cheese mixtures between noodles twice more. Spread 2 cups sauce evenly over top layer of noodles. Sprinkle evenly with remaining 1 1/2 cups mozzarella and 1/4 cup Parmigiano-Reggiano. Loosely cover with parchment-lined foil and transfer to a rimmed baking sheet.

Bake until noodles are tender but still al dente (easily pierced with the tip of a knife), 40 to 45 minutes. Uncover; continue baking until bubbly and puffed slightly along edges and golden brown in places on top, 20 to 25 minutes more. (There may appear to be a lot of liquid in the dish. It will be absorbed as the lasagna cools.) Transfer dish to a wire rack and let cool slightly and set, about 20 minutes; cut into squares to serve.

Heat oil in a large saucepan over medium-high. Add mushrooms and eggplant and saute 10 minutes. Add onion, carrots, celery, and 1 teaspoon salt; cook until vegetables have browned in places and most of moisture is cooked out of mushrooms and eggplant, about 15 minutes. Add garlic, oregano, and red-pepper flakes; cook until fragrant, 1 minute. Add tomato paste; cook 2 minutes more. Puree tomatoes in a blender or food processor; add to pan. Bring to a boil, then reduce heat to low and simmer, stirring occasionally, until reduced and thickened slightly but still very loose, about 15 minutes. Remove from heat.

In a large bowl, whisk together ricotta, milk, eggs, 1 cup Parmigiano-Reggiano, 2 1/2 cups mozzarella, parsley, 1 teaspoon salt, and 1/4 teaspoon pepper.
Spread 2 cups sauce evenly in a 9-by-13-inch baking dish, preferably ceramic or enameled cast iron. Arrange 3 lasagna noodles over sauce (space noodles evenly; they will expand as the lasagna cooks). Spread 2 cups cheese mixture over noodles; top with 3 more noodles. Repeat layering of vegetable and cheese mixtures between noodles twice more. Spread 2 cups sauce evenly over top layer of noodles. Sprinkle evenly with remaining 1 1/2 cups mozzarella and 1/4 cup Parmigiano-Reggiano. Loosely cover with parchment-lined foil and transfer to a rimmed baking sheet.