Heat the oven to 400°F. Prick the russet potatoes and bake on the rack until a knife slides in easily, 45–60 minutes.
Halve the hot potatoes, scoop out the flesh, and rice it onto a clean work surface; spread to release steam for 2–3 minutes.
Sprinkle the fine salt over the potatoes, add the large egg, and gently mix with a fork until just combined.
Sprinkle most of the all-purpose flour over the mixture, reserving a little for dusting; use a bench scraper and your hands to bring it together into a soft dough that just holds, kneading lightly for about 1 minute.
Dust the work surface with some reserved flour, divide the dough into 4 pieces, roll each into 3/4-inch-thick ropes, and cut into 3/4-inch pillows; if you like ridges, roll each piece over fork tines or a gnocchi board.
Bring a large pot of water to a rolling boil and add the kosher salt.
Melt the unsalted butter in a wide skillet over medium heat until foamy; add the fresh sage leaves and cook until fragrant and lightly crisp, 1–2 minutes; keep warm over low heat.
Boil the gnocchi in batches in the salted water, stirring gently, until they float and feel tender at the center, 1–2 minutes after floating; transfer with a slotted spoon directly to the sage-butter skillet, adding a splash of cooking water as needed; toss over medium heat for 1 minute to coat.
Serve immediately with Parmigiano Reggiano cheese, finely grated (for serving).