Heat oven to 425°F. Toss squash, onion and garlic with olive oil on a large rimmed baking sheet. Spread in one layer. Roast 25–35 minutes, stirring halfway, until squash is easily pierced and lightly golden. Remove garlic earlier if it begins to darken.

While vegetables roast, cook rigatoni in unsalted boiling water according to package directions until just tender with a firm bite. Reserve 1 1/2 cups cooking water before draining.

Transfer roasted vegetables and any oil to a deep pot. Add sage, salt, pepper and 3/4 cup reserved pasta water. Blend with an immersion blender, keeping the head submerged to avoid hot splashes. If using a countertop blender instead, cool slightly and follow its hot-liquid instructions; never seal hot liquid in a personal blender.

Add drained pasta to the sauce over low heat. Stir in 45 g Parmesan and lemon juice. Toss, adding more pasta water a few tablespoons at a time until the sauce coats the pasta smoothly. Divide into four bowls and finish with the remaining 15 g cheese.

Refrigerate leftovers in shallow containers within 2 hours, or 1 hour above 90°F. Keep at 40°F or below for 3–4 days. Reheat to 165°F, stirring in a splash of water to loosen the sauce.