Pour the water and milk into a 4-quart / 3.8 L heavy-bottomed pot, add 1 tsp salt, and bring to a gentle boil over medium-high heat, about 8 minutes.

Lower the heat to medium-low. Whisking constantly with one hand, pour in the polenta in a thin, steady stream, then keep whisking for 1 minute until no lumps remain. Switch to a wooden spoon.

Cook for 35 minutes at a slow bubble, stirring every 3 to 4 minutes and scraping the corners. It's done when it pulls away from the sides and tastes smooth with no grit. If it gets too thick, loosen it with 50 ml hot water at a time.

During the last 5 minutes, melt 40 g butter in an 18 cm / 7-inch skillet over medium heat. Add the sage leaves and cook for 2 to 3 minutes until the butter foams, turns pale amber and smells nutty, and the leaves crisp. Remove from the heat.

Take the polenta off the heat and stir in the remaining 40 g cubed butter and the Parmigiano until glossy. Taste, then add pepper and more salt if needed. Spoon into warm bowls, top with the sage butter and leaves, and serve within 10 minutes.