Heat the olive oil in a large heavy-bottomed pan over medium heat until it shimmers and begins to smell fragrant.
Add the diced pumpkin to the pan, sprinkle with a pinch of salt, and cook, stirring occasionally, until the pumpkin starts to turn golden brown and develops a deep caramel color, about 10 minutes. You’ll notice a smoky aroma and the pumpkin softens slightly.
Stir the Arborio rice into the pumpkin mixture, cooking for about 2 minutes, until the rice becomes slightly translucent around the edges and is coated with the oil and pumpkin juices.
Begin adding the warm vegetable broth one ladleful at a time, stirring constantly. Wait until each addition is mostly absorbed before adding the next, allowing the rice to release its starch and become creamy.
Continue this process, stirring gently and adding broth gradually, until the rice is tender and creamy, about 20 minutes. The pumpkin should be deeply golden and fragrant, and the mixture should have a warm, amber hue with a silky texture.
Finish by stirring in chopped fresh sage or thyme, if using, and adjusting seasoning with salt and pepper to taste. For extra crunch, sprinkle toasted seeds or nuts on top before serving.