Heat oven to 375°F. Use 1 teaspoon of the oil to grease a 9-by-13-inch baking dish. Bring a large pot of unsalted water to a boil. Cook pasta 2 minutes less than the package al dente time, usually about 9–10 minutes for ziti; it should still be slightly firm. Reserve 1 cup cooking water, then drain.

While pasta cooks, heat remaining 2 teaspoons oil in a large saucepan or Dutch oven over medium heat. Cook onion 5–6 minutes until softened. Add garlic, sage, nutmeg, salt, and pepper; stir 30 seconds. Add pumpkin, milk, and 1/2 cup reserved pasta water. Bring to a gentle simmer, stirring, and cook 3 minutes.

Remove sauce from heat. Stir in ricotta until combined, then squeezed spinach and drained pasta. Add more reserved water a little at a time until pasta is generously coated and easy to stir, up to the remaining 1/2 cup.

Transfer to the prepared dish and spread evenly. Sprinkle mozzarella and Parmesan over the top. Set dish on a rimmed sheet pan. Cover with foil, tenting it slightly so it does not rest on the cheese.

Bake covered 20 minutes, then uncover and bake 15–20 minutes more, until bubbling and the center reaches 165°F. The cheese should have golden patches. Let rest 10 minutes before dividing into 6 portions.

Refrigerate leftovers in shallow containers within 2 hours, or 1 hour above 90°F. Use within 3–4 days. Reheat covered with a splash of water until the center reaches 165°F.