Peel and dice the pumpkin into ½ inch cubes (1 cm). The smaller the pieces, the quicker they will roast, while also offering more corners for caramelization.
Toss the pumpkin pieces in ½ tablespoon olive oil, salt and pepper.
Roast the diced pumpkin at 400°F (200°C) for 20-25 minutes until tender and slightly caramelized.
Keep a handful of pieces aside for garnishing, if you like, and add the others to a blender until a smooth pumpkin puree is formed. Should you need it, use a little vegetable stock to make the blending process smoother.
Prepare the vegetable or chicken broth and keep it warm throughout the cooking process. You will be adding it to the risotto gradually, and it is important to maintain the temperature of the dish for even cooking.
Heat the remaining olive oil over medium heat in a large saucepan with a heavy bottom. Add the minced garlic and chopped onion. Sauté until translucent, approximately 3-4 minutes.
Add the rice and increase the heat to high. Toast and mix well until the rice grains change color and the edges turn translucent, approximately 2 minutes.
OPTIONAL: Add ¼ cup white wine and cook until it evaporates completely.
Reduce the heat the low.
Add one cup of hot stock, stirring frequently, until the rice has absorbed the liquid. Continue adding broth one cup at a time, allowing each addition to be absorbed before adding the next, until the rice is tender and creamy, approximately 20 minutes.
Once the rice is 75% cooked, add the pumpkin purée and sage.
Mix well and continue cooking until the rice is ready.
Once the pumpkin risotto is ready but still al dente, add the grated cheese and incorporate it well to the dish. Taste for seasoning and adjust if needed.
Allow the risotto to rest for a couple of minutes then serve it with the toasted chopped walnuts and some fresh herbs for garnish, such as parsley.