Roast the pumpkin. Preheat the oven to 400°F. Halve the pumpkin and scoop out the seeds. Place cut-side down on a baking sheet and roast for 30–45 minutes, until soft and easily pierced with a fork. Skip this step if using canned pumpkin.

Brown the sausage. Meanwhile, add the sausage to a large, wide skillet over medium heat without oil. Break it into pieces, leaving some larger chunks. Cook in its rendered fat, stirring occasionally, until cooked through with golden, crispy edges. Transfer to a plate, leaving the drippings in the pan.

Fry the sage. Add the sage leaves to the drippings and fry briefly until crisp, about 20–30 seconds. Remove and set aside. Pour off excess fat if necessary, retaining enough to coat the pan and keeping the browned bits.

Start the risotto. Add the shallot and 1 tablespoon butter to the skillet. Sauté over medium-low heat for 2–3 minutes, until softened. Add the rice and stir for about 2 minutes to toast. Meanwhile, warm the stock in a separate saucepan and keep at a gentle simmer.

Deglaze with wine. Add the wine and scrape up the browned bits from the pan. Stir until mostly absorbed.

Add the stock gradually. Add warm stock a ladle at a time, stirring frequently and letting each addition become mostly absorbed before adding more. Maintain a gentle simmer and begin checking the rice after about 15 minutes.

Prepare the pumpkin purée. Scoop the roasted pumpkin flesh into a blender or a container suitable for an immersion blender. Blend with a little warm stock until smooth. Season with salt and nutmeg, then measure out 1 cup. If using canned pumpkin, season 1 cup of purée and loosen with a little warm stock.

Finish cooking the rice. When the rice is about three-quarters cooked, stir in the pumpkin purée. Continue adding stock or warm water until the rice is al dente, generally 18–25 minutes total from the first stock addition. Keep the consistency creamy and loose.

Make it glossy. Turn off the heat. Add 1 cup Parmigiano and the remaining 2 tablespoons butter. Stir vigorously until melted and glossy. Taste and adjust the salt, adding more warm stock or water if needed.

Plate and serve. Spoon into bowls and top with sausage, fried sage, extra Parmigiano, and chili oil, if using. Serve immediately.