PREP: Preheat oven to 400F. Peel squash, cut in half, and remove seeds. Cut squash into small pieces, approximately ¾-inch in size. Peel + slice shallot (or onion) and peel garlic cloves.
TOSS: Place cubed squash, shallot, and garlic cloves in a large baking dish. Toss in olive oil, thyme, salt, and pepper.
ROAST: Roast squash and seasonings in the oven for 30-35 minutes, tossing halfway, until the squash is easily pierced with a fork.
COOK PASTA (optional): Cook enough pasta for 4-6 servings in a large pot of salted water. Be sure to reserve up to 2 cups of the pasta water before draining.*If you're not making this sauce alongside pasta, you can skip this step and use veggie broth instead!
BLEND: Transfer the roasted squash, onion, garlic, and all the seasonings into a high-speed blender. Add fresh parsley, parmigiano-reggiano, and 1.5 cups of pasta water or broth. Blend until smooth, using your blender's tamper to push ingredients down.
ADJUST: Adjust seasonings to taste, adding more salt, pepper, or thyme. You can also add more broth or pasta water if you'd prefer a thinner consistency.
SERVE OR STORE: Stir sauce into warm cooked pasta, or store in the fridge for later!
