Warm the broth and water together in a saucepan over low heat and keep hot, not rapidly boiling. Have extra hot water available. Measure pumpkin and grate cheese before starting the rice.

Heat olive oil in a wide heavy 3- to 4-quart saute pan over medium heat. Cook onion 4–5 minutes until translucent. Add garlic for 30 seconds, then add dry Arborio rice and stir for 2 minutes to coat the grains.

Add about 1/2 cup hot broth mixture and cook at a steady gentle simmer, stirring often, until mostly absorbed. Continue adding liquid about 1/2 cup at a time. Stir across the bottom to prevent sticking, but do not let the rice scorch dry between additions.

After about 18 minutes of adding liquid, begin tasting the rice. When nearly tender with a slight bite, stir in pumpkin and sage. Continue cooking with small additions of hot liquid for another 3–5 minutes, until the rice is tender but not mushy. Total rice cooking is usually 22–28 minutes; add extra hot water if needed.

Remove from heat and stir in butter, Parmesan, and pepper. Add a splash of hot water if needed so the risotto spreads gently rather than standing in a stiff mound. Taste before adding any optional extra salt, since broth and cheese already contain salt. Serve immediately in four portions with reserved cheese and a pinch of chopped sage.

Refrigerate leftovers in shallow containers within 2 hours, or 1 hour above 90°F. Use within 3–4 days. Reheat with a little water, stirring until all of the portion reaches 165°F.