Cook the potatoes in a saucepan of lightly salted boiling water for 10–12 minutes until tender. Drain, return the potatoes to the pan and heat gently for several seconds to dry out. Mash the potatoes and beat in the egg, salt, oil and flour to form a sticky dough.
Take walnut-sized pieces of the dough and roll into egg shapes, rolling them over the tines of a fork.
Bring a large saucepan of lightly salted water to a rolling boil, add half the gnocchi (freeze the remainder for later use) and cook for 3 minutes until they rise to the surface. Drain the gnocchi and transfer to serving bowls.
Meanwhile, melt the butter in a frying pan. As soon as it stops foaming, add the sage and fry over a medium-high heat, stirring, for 2–3 minutes until crisp and the butter turns golden brown. Drizzle over the gnocchi, scatter with grated Parmesan and serve immediately.