Boil the potatoes in their skins in a large pot of water for 25 minutes or until tender.

Drain potatoes, then peel them while still warm. Pass them through a ricer or mash until very smooth into a mixing bowl.

Let the mashed potatoes cool slightly, then add the flour, egg, and salt. Mix using your hands or a fork until a soft dough forms—do not overwork.

Turn the dough onto a lightly floured surface. Divide into 4 pieces. Roll each piece into a long rope about 2 cm diameter.

Cut ropes into 2 cm pieces. Lightly roll each piece over the back of a fork for classic ridges (optional).

Bring a large pot of salted water to a gentle boil. Drop in the gnocchi in batches. When they float to the surface (about 2-3 minutes), remove them with a slotted spoon.

Meanwhile, melt the butter in a skillet over medium heat. Add sage leaves and cook until the butter is foamy and fragrant but not browned (about 2 minutes).

Add drained gnocchi to the skillet and toss gently for 2-3 minutes to coat in sage butter.

Season with salt and pepper. Serve immediately, topping each dish with grated Parmesan.