Pour the chicken stock and pumpkin purée into a saucepan. Stir until smooth and then place over medium-low heat. Bring to a simmer and keep warm.
Set a large pot or dutch oven over moderate heat. Once hot, drizzle in the olive oil and add the sausage. Use a wooden spoon to break up the sausage. Cook until browned and slightly crispy. Use a slotted spoon to transfer the sausage onto a plate.
Add in the sliced mushrooms and thyme leaves. Cook, stirring often, until the mushrooms have browned. Add the shallot and garlic and cook for a few minutes longer. Add the rice and cook a bit to develop the flavor. Deglaze the pan with the wine, scraping up the bottom to release all of those bits and pieces.
Stir in a ladleful of the warmed pumpkin stock and cook, stirring often, until the liquid has just about evaporated. Continue adding the stock, a ladleful at a time, cooking until evaporated. Do this until all of the stock has been used up and the rice is tender, about 20 to 25 minutes. Once done, return the sausage to the pot, along with the butter, parmesan, parsley, and sage. Season to taste with salt and pepper.
Spoon into serving bowls and top with more parmesan and parsley for garnish. Enjoy!