Step 1

Heat butter or olive oil in a 5- to 6-quart heavy pot over moderately high heat, then add chopped sage (or bundle, see notes above) and cook until fragrant, about 15 seconds. Add cubed squash, diced onion, 1.5 cups water, 3/4 teaspoon salt, and pepper to taste. If your squash pieces are not submerged in water, add more water just until they are barely covered. Simmer, uncovered, stirring occasionally, until squash is very tender and water has reduced considerably, about 15 to 20 minutes depending on the size of the squash pieces.

Step 2

While squash mixture simmers, cook pasta in a 6- to 8-quart pot of boiling salted water with a large pinch of kosher salt until al dente. Reserve a few cups of pasta cooking water, then drain pasta in a colander.

Step 3

When squash is knife tender, it’s done. Turn off the heat. If you didn’t chop up the sage, extract what is left of the bundle you added to the pot — a few small leaves remaining is fine. If you have an emersion blender, purée mixture right in pot. If you don’t, transfer mixture to a food processor or blender and purée until smooth. Taste sauce. Add more salt if necessary. Add a grating of fresh nutmeg if you wish. The sauce should be thick enough to coat the back of a spoon. If it is too thin, simmer over low heat until it thickens. If it’s too thick, thin with some of the reserved pasta cooking liquid until it is the right consistency.

Step 4

If you wish, stir in Parmigiano-Reggiano. (Note: I do not do this — the mixture tastes wonderful without any cheese, so I just serve the cheese on top of the pasta or I omit it if serving to vegan friends.)

Step 5

Place pasta in a serving bowl. Toss with enough butternut-sage sauce to coat nicely. Add a handful of parmesan cheese. If necessary, add a little bit of the reserved cooking water to thin it out. Shave parmesan and crack pepper over each bowl before serving.

Step 6

If you have extra sauce, store it in the fridge for a later date. The sauce thickens as it sits, so on subsequent uses, it will most likely be necessary to use the reserved cooking liquid to thin out.