Preheat the oven to 400 degrees.
On a large baking sheet lined with parchment paper toss the 1 small butternut squash, 5 cloves garlic, and 1 large yellow onion, with the 1/4 cup olive oil, 1 tbsp thyme, 1 tsp paprika, 2 tsp salt, 2 tsp black pepper, and 1/2 tsp cumin until evenly coated.
1/4 cup olive oil, 1 small butternut squash, 5 cloves garlic, 1 large yellow onion, 1 tbsp thyme, 1 tsp paprika, 2 tsp salt, 2 tsp black pepper, 1/2 tsp cumin
Bake for 40 minutes until the squash is browned and tender.
Transfer the mixture to a blender along with the 1/2 cup vegetable broth. Blend until a smooth puree forms.
1/2 cup vegetable broth
Meanwhile, boil a pot of water on the stove and heavily salt. Add the 12 oz pasta and cook for about 8 minutes until al dente.
12 oz pasta
Drain and set aside, reserving 1/2 cup of the pasta water.
Start the sauce by melting the 6 tbsp salted butter in a large saucepan on medium heat. Once melted, stir in the 6 tbsp all purpose flour and cook for about 5 minutes, stirring constantly until the mixture is golden brown.
6 tbsp salted butter, 6 tbsp all purpose flour
Pour in the 2 cups whole milk and 3/4 cup half and half and stir until incorporated. On medium-high heat, bring the mixture to a heavy simmer and stir occasionally until thickened, about 5 minutes.
2 cups whole milk, 3/4 cup half and half
Stir in the 1 cup sharp cheddar cheese, 1 cup gouda cheese, 1/2 cup havarti cheese, and butternut squash puree until a smooth sauce forms. If the sauce is too thick, add in the reserved pasta water.
1 cup sharp cheddar cheese, 1 cup gouda cheese, 1/2 cup havarti cheese
Pour the cooked pasta into the sauce and stir until evenly coated.