Place squash into a steamer basket in a saucepan; fill with water to just below the bottom of the basket. Cover, bring to a boil, and steam squash until tender, 10 to 15 minutes. Drain; use a fork to mash squash in a bowl.
Melt butter in a saucepan over medium-high heat. Add minced shallot; cook and stir for 2 minutes until shallot is translucent, then stir in rice. Continue cooking and stirring until rice is glossy and the onion begins to brown on the edges, it should start to smell toasty, about 5 minutes more.
Pour in white wine; cook, stirring constantly, until it has evaporated. Stir in mashed squash and 1/3 of the hot chicken stock; reduce heat to medium
Cook and stir until chicken stock has been absorbed into rice, 5 to 7 minutes. Add 1/2 of the remaining chicken stock, and continue stirring until it has been absorbed. Finally, pour in remaining stock, and heavy whipping cream and continue stirring until the risotto is creamy.
Stir in Parmesan cheese and season with salt and pepper.