Preheat the oven to 425°F and line a baking sheet with parchment paper.
Drizzle the squash with olive oil, sprinkle with salt and pepper, and place cut-side down on the baking sheet. Wrap the shallot and garlic cloves in foil with a drizzle of olive oil and a pinch of salt and place on the baking sheet. Roast for 30 minutes or until the squash is soft.
Scoop 1 cup of the squash flesh and transfer to a blender with the shallot, peeled garlic, water, cashews, 2 tablespoons olive oil, nutritional yeast, vinegar, sage, thyme, ¾ teaspoon salt, and several grinds of black pepper. Blend until creamy.
Cook the pasta according to package directions in a pot of salted boiling water. Reserve 1 cup of the hot pasta water.
Drain the pasta and return to the pot. Stir in the sauce, adding 1/2 to 1 cup of the reserved pasta water to loosen the sauce and coat the pasta. Season with ¼ to ½ teaspoon salt. Top with freshly ground black pepper, a few thyme leaves and sautéed broccoli, if desired.