Preheat oven to 425°F (220°C). Toss squash cubes with olive oil, thyme, salt, and pepper. Spread in a single layer on a baking sheet. Roast for 25-30 minutes until golden and caramelized at the edges. Set aside — half will go into the risotto, half on top.

Pour broth into a medium saucepan and keep at a bare simmer over low heat throughout the entire cooking process. Adding cold broth to hot rice disrupts cooking.

In a wide heavy-bottomed pot, heat 2 tbsp butter and 1 tbsp olive oil over medium-low heat. Add shallots and cook, stirring, for 6-8 minutes until very soft and translucent. Add garlic and cook 1 more minute.

Add Arborio rice. Stir to coat every grain in fat. Toast for 2 minutes until the edges of the rice become slightly translucent and smell faintly nutty.

Pour in white wine. Stir constantly until fully absorbed, about 1-2 minutes.

Add one ladleful of warm broth (about 3/4 cup). Stir almost constantly over medium heat. When liquid is nearly fully absorbed, add another ladle. Continue for 20-25 minutes until rice is al dente — tender with just a tiny bite in the center, and the consistency is loose and flowing like lava.

Mash or roughly purée half the roasted squash and stir into the risotto during the last 5 minutes. This naturally thickens and sweetens the risotto.

Remove pot from heat. Add 2 tbsp cold butter cut into small pieces and all the Parmigiano-Reggiano. Stir vigorously for 1-2 minutes — the risotto should become incredibly creamy and glossy. Add nutmeg, taste, and season generously with salt and white pepper.

Melt 4 tbsp butter in a small skillet over medium heat. Once golden brown and nutty smelling, add sage leaves. They will crisp in 30-45 seconds. Remove immediately and drain on paper towels.

Spoon risotto into warm wide bowls. Top with reserved roasted squash, crispy sage, a drizzle of brown butter from the pan, and extra Parmigiano. Serve within minutes — risotto cannot wait.