Prepare the vegetable broth and heat it in a casserole.
Pour the olive oil in a large deep pan over a medium flame. Dice the onions and place them into the heated pan. Continue to cook the onions for a few minutes until the onions become translucent.
Add the arborio rice to the pan. Stir and let saute while stirring for about a minute. The rice will begin to look translucent. (It's important not to wash the rice before cooking as the starch on the outside of the rice kernels will help to give the risotto a creamy texture).
Add the sage leaves and the white wine and keep stirring. Continue to cook a few minutes over the medium flame until the wine has cooked into the rice.
Reduce the flame. Start slowly adding the vegetable broth, one ladle at a time. After each ladle, stir gently the rice until it absorbs most of the broth. Continue with the ladles until most of the broth has been used (about 15 minutes). You can add the excess pumpkin liquid along with one of the ladles. The rice should be soft with a slight firmness.
Add the pureed pumpkin and mix it gently into the rice for 1-2 minutes over the low flame.
Remove the pan from the flame and add the Pecorino and Parmesan cheeses as well as the butter. Gently stir these into the risotto. Cover the pan and let sit a couple minutes as the cheese and butter melt into the risotto.
Adjust seasoning with salt and pepper. Add more sage if needed, but watch out since a little goes a long way.
If you are adding mushrooms, saute them in a little olive oil in a separate pan. Before serving, place the mushrooms over the top of your risotto dish.
Serve and enjoy the risotto while it's hot!