First, heat the oven to 400F. Toss the cubed squash with the olive oil and 1/2 teaspoon salt, spread it on a sheet pan in one layer, and roast for about 25 minutes, until the edges have browned and a fork meets no resistance.

Set aside a third of the cubes. Blend the remaining two thirds until completely smooth, adding a ladle of stock if the blender needs help.

Whisk that puree into the stock in a saucepan and hold it at a bare simmer beside the risotto pan. Cold stock stalls the rice, which is the usual reason risotto takes twice as long as it should.

Next, melt 3 tablespoons of the butter in a wide, heavy pan over medium heat. Cook the shallots gently for 5 minutes until soft and translucent, then add the garlic and cook for 1 minute more.

Then add the rice and toast it for 2 minutes, stirring, until the grains look glassy at the edges with a white dot at the center. Do not rinse the rice at any point, because that surface starch is the only thing that will make the dish creamy.

After that, pour in the wine and stir until it has almost disappeared. Add the hot pumpkin stock one ladle at a time, stirring every twenty to thirty seconds and waiting for each addition to be absorbed before the next goes in.

Keep going for 18 to 22 minutes. The rice is ready when a grain is tender through with only the faintest firmness at the center and no chalky white core.

Finally, stir the reserved roasted cubes back in, then pull the pan off the heat. Beat in the cold butter, the parmesan, the nutmeg, 1 1/2 teaspoons salt and the pepper for a full minute, which is the step that emulsifies the fat into the starch.

Shake the pan. The surface should ripple like slow lava and settle flat, and if it moves as one mass, loosen it with a little more hot stock. Serve at once, with sage leaves and more parmesan.