Step 1
Preheat an oven to 450 degrees F (230 degrees C). Line a baking sheet with aluminum foil.
Step 2
Place squash cut-side up on the prepared baking sheet. Cover squash with aluminum foil.
Step 3
Bake in the preheated oven until squash is tender 45 minutes to 1 hour 15 minutes.
Step 4
Heat 1 1/2 teaspoons olive oil in a skillet over medium heat; cook and stir mushrooms and garlic in the hot oil until mushrooms are tender 5 to 10 minutes. Remove skillet from heat.
Step 5
Heat remaining 1 1/2 teaspoons olive oil in a separate skillet over medium heat; cook and stir onion in the hot oil until softened about 5 minutes. Add spinach to onion; cook until spinach is heated through 3 to 5 minutes. Remove skillet from heat.
Step 6
Heat 6 cups milk in a 5-quart saucepan over medium heat; cook and stir until milk is simmering about 5 minutes. Whisk remaining 1 cup milk and cornstarch together in a bowl until smooth; stir into simmering milk. Bring milk mixture to just under a boil stirring constantly with a wooden spoon and scraping bottom of pot to prevent scorching until milk mixture has thickened into a sauce about 5 minutes; remove pot from heat.
Step 7
Whisk 1 1/2 cups Parmesan cheese honey nutmeg sage salt and pepper into sauce until smooth. Cover pot with a lid and keep warm over low heat.
Step 8
Bring a large pot of lightly salted water to a boil. Cook lasagna noodles in the boiling water stirring occasionally until cooked through but firm to the bite about 8 minutes. Drain.
Step 9
Reduce oven temperature to 375 degrees F (190 degrees C).
Step 9
Scrape flesh from butternut squash into a bowl; stir with a fork until evenly mashed. Stir ginger salt and pepper into mashed butternut squash.