Preheat the oven to 425°F and line a baking sheet with parchment paper.
Drizzle the squash with olive oil, season with salt and pepper, and place cut side down on the baking sheet.
Wrap the shallots and garlic cloves in foil with a drizzle of olive oil and a pinch of salt, then place on the baking sheet.
Roast the squash, shallots, and garlic for 30 minutes, or until the squash is soft.
Scoop 1 cup of roasted squash flesh into a blender along with the roasted shallots, peeled garlic, water, cashews, 2 tablespoons olive oil, nutritional yeast, balsamic vinegar, sage, thyme, ¾ teaspoon salt, and fresh black pepper.
Blend until smooth and creamy.
Cook the pasta according to package directions in salted boiling water.
Reserve 1 cup of hot pasta water, then drain the pasta and return it to the pot.
Stir the creamy squash sauce into the pasta, adding ½ to 1 cup of reserved pasta water to loosen the sauce and coat the noodles.
Season with ¼ to ½ teaspoon salt and freshly ground pepper.
Garnish with additional thyme leaves and serve with sautéed broccoli if desired.