Butternut Squash Lasagna

For the butternut squash:

• 2 lbs butternut squash, peeled, seeded, and cut into 1-inch cubes
• 2 tablespoon olive oil
• Kosher salt and black pepper, to taste
• 1/2 cup vegetable broth
• 1 tablespoon pure maple syrup
• 1/8 teaspoon ground nutmeg

For the lasagna:

• 12 lasagna noodles*
• 3 cups shredded mozzarella cheese, divided
• 1/4 cup freshly grated Parmesan cheese

For the spinach ricotta mixture:

• 2 tablespoons butter
• 1 shallot, minced
• 4 garlic cloves, minced
• 4 cups packed spinach
• 15 oz ricotta cheese
• 1/4 cup Parmesan Cheese
• 1 large egg
• 1 teaspoon fresh sage, minced
• 1 teaspoon fresh thyme, minced
• 1/4 teaspoon crushed pepper flakes
• Kosher salt and black pepper, to taste

For the bechamel sauce:

• 1/4 cup butter
• 1/4 cup all-purpose flour
• 3 1/2 cups whole milk
• Kosher salt and black pepper, to taste