5 1/2 to 6 cups homemade or low-sodium chicken or vegetable stock
1 cup pumpkin purée (not pumpkin pie filling)
2 teaspoons kosher salt
1 teaspoon freshly ground black pepper
1/2 teaspoon ground nutmeg, or 6 to 10 scrapes on a grater from a whole nutmeg
8 tablespoons (4 ounces) unsalted butter
8 ounces shallots (7 to 8), minced
1 3/4 cups arborio, carnaroli, or vialone nano rice
1 1/2 cups dry white wine, Italian preferred, such as Pinot Grigio or Pinot Bianco, or dry white vermouth
1 1/4 cups grated Parmesan cheese
6 to 10 large sage leaves, finely chopped (optional)
Place the stock, pumpkin, salt, pepper, and nutmeg in a medium saucepan over high heat on a burner near the one where you'll be cooking the risotto. Stir to combine and bring to a gentle boil. Reduce the heat to a steady simmer.
Set a large saucepan next to the first one on the stovetop, add the butter, and melt over medium heat. Add the shallots and cook, stirring, until they are translucent with a few brown edges, 6 to 7 minutes.
Add the rice and stir until each grain is coated in fat, 2 to 3 minutes. Reduce the heat to low. Add the wine or vermouth and cook, stirring constantly, until it is absorbed.
Add 1/2 cup of the pumpkin stock mixture and stir constantly until absorbed. Add the remaining stock mixture, 1/2 cup at a time, stirring constantly after each addition and adding the next amount only after the previous one is fully absorbed by the rice.
After you have used about 4 1/2 to 5 cups of the stock mixture (this will be about 30 to 35 minutes after you started adding the first 1/2 cup of stock), taste the rice to determine if it is very hard, firm, or al dente. You are looking for al dente, with the grains just a bit toothsome (a little resistant to the bite) but cooked — not hard or powdery. The rice should be enrobed in a creamy sauce and the grains should remain slightly al dente. If it is, you can move on to the next step. But it hasn't reached that stage, add more stock, this time 1/4 cup at a time, stirring after each addition and tasting once it has been absorbed. It should take about 45 minutes for all of the stock mixture to be added and incorporated, but you might not need all of it, so it's important to slow down to 1/4 cup at a time and taste every few minutes.
Stir in the cheese and sage if using. Serve immediately. Risotto is not a make-ahead dish.