Preheat oven to 375 degrees F. Line a 15x10x1-inch baking pan with parchment paper; set aside. Coat a 2-quart square baking dish with cooking spray; set aside.
Coat the cut sides of the butternut squash with cooking spray; place squash halves, cut sides down, on the prepared baking sheet. Roast for 40 to 45 minutes or until squash is very tender and cooked through. Remove from oven; let stand until cool enough to handle. Scoop flesh from squash halves; discard skin. Using a potato masher, mash the squash; set aside.
Meanwhile, cook pasta according to package directions. Drain well.
In a medium saucepan melt butter over medium heat. Whisk in flour, salt, and white pepper until combined. Add milk, whisking until smooth. Cook and stir until thickened and bubbly. Add semisoft cheese; whisk until cheese is melted. Stir in mashed squash. Add cooked pasta; stir until coated.
Place half of the pasta mixture in the prepared baking dish. Evenly sprinkle half of the mozzarella cheese and half of the cheddar cheese on top of the pasta. Arrange half of the Muenster cheese over all. Repeat layers. Bake in the 375 degrees F oven about 25 minutes or until cheese is golden brown.