Bring the vegetable stock to a bare simmer in a saucepan and keep hot for ladling.
Warm the extra-virgin olive oil in a wide, heavy pot over medium heat.
Add the onion and fresh sage leaves; cook, stirring, until the onion is translucent and fragrant, 4–5 minutes.
Stir in the pumpkin and cook until the edges are just tender but not breaking down, 6–8 minutes.
Add the arborio rice and cook, stirring, until the grains are coated and lightly toasted, 1–2 minutes.
Pour in the dry white wine and stir until mostly absorbed, 1–2 minutes.
Add a ladleful of the hot liquid, stirring frequently; maintain a gentle simmer and continue adding more as each addition is absorbed, until the rice is al dente and suspended in a creamy sauce, 18–22 minutes.
Off the heat, stir in the unsalted butter and Parmigiano Reggiano until glossy and emulsified; season with the kosher salt and black pepper. If needed, loosen with a splash of the hot liquid to reach a softly flowing consistency. Cover and rest 2 minutes.