Roast the squash
Preheat your oven to 400°F (200°C). Toss acorn squash cubes with 1 tablespoon olive oil, salt, and pepper. Spread on a baking sheet and roast for 25–30 minutes or until soft and slightly golden.
Sauté the aromatics
In a pan, heat 1 tablespoon olive oil. Add onion and garlic and cook for about 5 minutes until soft and fragrant. Stir in thyme, sage, and red pepper flakes. Remove from heat.
Blend the sauce
Transfer roasted squash and sautéed aromatics into a blender. Add vegetable broth, Parmesan, and milk. Blend until smooth and creamy. Adjust salt and pepper to taste.
Cook the pasta
Bring a large pot of salted water to a boil. Cook pasta according to package instructions. Drain, but save about ½ cup of pasta water.
Combine and serve
In a clean skillet, melt butter. Pour in the squash sauce and stir until warmed through. Add cooked pasta and toss to coat. Use pasta water to loosen the sauce if needed. Serve hot with extra Parmesan and fresh herbs on top.