With the heat still on medium-high, add the butter and let melt. Add the onion and cook until translucent, about 2 minutes. Add the garlic and cook, stirring constantly until fragrant, about 30 seconds.
Add the rice and sage and cook, stirring constantly, until rice starts to look translucent, about 1 minute. Add the wine or broth and cook until mostly evaporated, about 1 minute (don't forget to scrape up those brown bits).
Stir in the pumpkin and chicken broth. As soon as it starts to simmer, snuggle in the chicken breasts. Cover the pan with a lid (or foil) and transfer to the oven.
Bake until chicken is cooked through and rice is tender with a firm bite, 20 to 25 minutes. Most of the liquid should be absorbed at this point but it will still look saucy.
Transfer the chicken to a cutting board, cover with foil, and let rest 5 minutes.
Meanwhile, stir the Parmesan into the rice. If it's too thick, add a splash of hot water. If needed, season with additional salt and pepper.
Slice the chicken breast and nestle the pieces into the risotto.