Preheat an oven to 400 degrees F (200 degrees C). Lightly oil a baking sheet.
Toss diced pumpkin with 2 tablespoons olive oil, sage, salt, and black pepper in a bowl. Spread evenly onto the prepared baking sheet.
Bake in the preheated oven, turning once midway through cooking, until pumpkin begins to brown, about 25 minutes.
Melt butter and remaining 1 tablespoon olive oil in a saucepan over medium heat. Add shallot; cook and stir until soft and translucent, about 5 minutes. Add rice and stir until the rice is coated in oil and has started to toast, 2 to 3 minutes. Add 3 1/2 cups chicken broth, 1/2 cup at a time, stirring slowly after each addition until absorbed into the rice. Add the roasted pumpkin. Stir in the remaining 1/2 cup chicken broth until mostly absorbed and rice is tender; adding the broth should take about 20 minutes total. Turn off heat and stir in the Parmesan cheese.