Step 1

Preheat oven to 400°. Place squash and 3 tablespoons oil in a large bowl; season generously with salt and pepper and toss to evenly coat squash. Transfer to 2 rimmed baking sheets, spreading out in a single layer, overlapping slightly. Roast until tender but not mushy, about 15 minutes. Let cool.

Step 2

Quickly blanch broccoli rabe in a large pot of boiling salted water just until it wilts, 1–2 minutes. Drain; briefly cool under running water. Squeeze out excess water; coarsely chop and transfer to a large bowl. Season with salt, pepper, and red pepper flakes; drizzle with oil and toss to coat.

Step 3

Mix mozzarella and next 5 ingredients in a large bowl; season with salt and pepper. DO AHEAD Squash, broccoli rabe, and cheese mixture can be made 1 day ahead. Cover separately and chill.

Step 4

Melt butter in a large heavy saucepan over medium heat. Add flour; stir until slightly thickened (do not allow mixture to turn brown), 2–3 minutes. Increase heat slightly; slowly whisk in 5 cups half-and-half, 1/2-cupful at a time, allowing béchamel to thicken between additions (adding half-and-half gradually will help to prevent lumps from forming). Add 1/8 teaspoon nutmeg and bay leaf.

Step 5

Reduce heat to low and cook, thinning with more half-and-half if too thick, until sauce is a milk shake–like consistency, about 10 minutes longer. Season to taste with salt and pepper. Strain through a fine-mesh sieve into a medium metal bowl. Set bowl over a large saucepan of gently simmering water. Cover and keep warm.

Step 6

Cook lasagna noodles in a pot of well-salted boiling water until still quite al dente, 8–9 minutes. Transfer immediately to a large bowl of ice water to cool. Drain; spread out noodles on a kitchen towel or baking sheets lined with parchment paper, placing a kitchen towel or parchment between layers.

Step 7

Ladle about 1/4 cup béchamel into a 13x9x2-inch baking dish; spread evenly over bottom. Line dish with a single layer of noodles, cutting as needed to fit (use large scraps in subsequent layers). Layer 1/3 of squash over. Scatter 1/3 of broccoli rabe over. Dollop 1/3 of ricotta mixture randomly over greens. Drizzle 1/2 cup béchamel evenly over ricotta mixture. Repeat process 2 more times for a Total of 3 layers, finishing with a layer of noodles. Spread remaining béchamel over; top with Parmesan. DO AHEAD Lasagna can be assembled 1 day ahead. Cover and chill. Return to room temperature before continuing.

Step 8

Preheat oven to 375°. Bake lasagna uncovered until bubbly and starting to brown, about 45 minutes. Turn oven to broil. Cook until browned and golden, 4–7 minutes. Let rest for 20–30 minutes before serving.