Transfer to a rimmed baking sheet or dish and roast until very tender, 30 to 45 minutes. Let stand until cool enough to handle, about 20 minutes, then separate the garlic cloves and squeeze the contents into a bowl.

2. In a small saucepan, heat 1 tablespoon olive oil over medium heat. Add the chopped onion, season with salt and cook, stirring, until softened and translucent, 5 to 6 minutes. Add the roasted garlic cloves, lemon juice, 1/3 cup water and ¼ teaspoon salt and bring to a boil over high heat; cook until the liquid is almost cooked off, about 5 minutes. Add the milk and bring just to a boil, then immediately lower the heat to medium so it simmers and cook, stirring occasionally, until just thickened, 10 to 15 minutes. Transfer to a blender and puree until smooth.

3. In a large dutch oven skillet, heat the remaining ¼ cup olive oil over medium heat. Add the finely chopped onion and cook, stirring, until soft to the bite, 9 to 11 minutes. Add the squash, ¼ cup water, 1 teaspoon salt and ¼ teaspoon pepper and bring to a boil. Cover with a lid, then lower the heat to a simmer, about medium heat. Cook, stirring every 5 minutes, until the squash is tender, 15 to 18 minutes.

3. Bring a large pot of salted water to a boil. Add the pasta and cook according to label directions until al dente. Meanwhile, uncover the squash and increase the heat to high. Cook, stirring once or twice, until the liquid is cooked off and the squash is just beginning to brown, 8 to 10 minutes. Pour the roasted garlic sauce into the skillet, turn off the heat and stir to combine; season generously with pepper.

4. Reserve ½ cup of the pasta cooking water, then drain. Stir the pasta into the butternut squash mixture, adding some pasta cooking water to loosen as needed. Serve topped with parmesan and black pepper.