Place the stock, pumpkin, nutmeg, a sprinkling of salt and pepper in a medium saucepan over high heat, Stir to combine and bring to a gentle boil. Reduce the heat to a simmer.
In a large, deep pan add the butter, and melt over medium heat. Add the shallots and cook, stirring until they are translucent. Add the rice and stir until each grain is coated in fat, 2 to 3 minutes. Reduce the heat to low. Add the wine or vermouth and cook, stirring constantly, until it is absorbed.
Add 1/2 cup of the pumpkin stock mixture and stir constantly until absorbed. Add the remaining stock mixture, 1/2 cup at a time, stirring constantly after each addition and adding the next amount only after the previous one is fully absorbed by the rice.
After you have used about 4 1/2 to 5 cups of the stock mixture taste the rice to determine if it is al dente. Continue to add more stock, if necessary, to reach al dente.
Stir in the cheese and sage if using. Serve immediately.