Step 1

Preheat oven to 375°. Grease a large 13x9" baking dish with extra-virgin olive oil. Heat ¼ cup extra-virgin olive oil in a medium saucepan over medium. Add 5 garlic cloves, finely chopped, and cook, stirring, until beginning to brown around edges and fragrant, about 2 minutes. Add one 28-oz. can whole peeled tomatoes and ¼ tsp. crushed red pepper flakes and crush tomatoes with a wooden spoon to form a mostly smooth sauce. (If your tomatoes are on the firmer side, use kitchen shears or a potato masher to break up.) Season with 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt and cook until mixture is thickened and flavors have come together, 15–17 minutes. Transfer to a 4-cup heatproof measuring glass and, stirring constantly, pour in water to make 3 cups sauce.

Step 2

Meanwhile, mix one 16-oz. package frozen chopped spinach, thawed, drained, one 16-oz. container whole-milk ricotta, 4 oz. cream cheese, room temperature, and 3 oz. Parmesan, finely grated, in a large bowl to combine, then mix in 1½ cups heavy cream. Season with freshly ground black pepper and add remaining 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt.

Step 3

Pour a scant ½ cup tomato sauce into prepared baking dish and spread into a thin layer just to coat. Place 3 dried lasagna noodles in a single layer on top. Spread 1 cup spinach mixture over evenly. Pour ½ cup sauce on top and spread over evenly. Starting with another layer of noodles, repeat process to create 4 more layers. Sprinkle a thin layer of finely grated Parmesan on top and cover pan with foil.

Step 4

If not making ahead, bake lasagna 45 minutes. Heat broiler. Uncover lasagna and broil until top is golden brown and bubbly, about 4 minutes.Do ahead: Lasagna can be assembled 3 months ahead; cover tightly and freeze. Bake, covered, in a 375° oven 45 minutes. Uncover and bake 10 minutes more. Broil about 3 minutes.