Gather all ingredients.

Bring a large pot of salted water to a boil over high. Add pasta and cook according to package directions for al dente. Drain, reserving 1 cup of pasta cooking water; set pasta aside.

While pasta cooks, melt butter in a large Dutch oven over medium. Add butternut squash, thyme, salt, and pepper, and cook, stirring occasionally, until browned on all sides, about 6 to 8 minutes.

Stir in milk, onion powder, garlic powder, cayenne, nutmeg, and turmeric and bring to a boil over high, stirring occasionally. Reduce heat to medium, cover, and cook, stirring occasionally, until squash is tender, about 6 minutes.

Transfer squash mixture into a blender and add Dijon mustard. Secure lid on blender, and remove center piece to allow steam to escape. Place a clean towel over opening. Process until very smooth, about 30 seconds.

Add pasta and pureed squash mixture to Dutch oven; gently heat over medium until pasta is warmed through, about 2 minutes.

Stir in Cheddar, Gouda, and Parmesan and cook over low, stirring constantly, until smooth, about 1 minute. Stir in 1/4 cup of the reserved pasta cooking water. Cook, stirring often, and add remaining cooking water, 1/4 cup at a time, as needed, until sauce is creamy and clings to pasta, 2 to 3 minutes. Season with additional salt to taste.