1Place potatoes in a large pot. Add water to cover by 1"; bring to a boil, reduce heat to medium, and simmer until tender, 25–30 minutes. Drain; set aside and let cool slightly. Peel potatoes. Pass through ricer or a food mill or sieve, into a large bowl. Whisk egg and egg yolk in a small bowl to blend. Add egg mixture, 1/3 cup Parmesan, 1 cup flour, 1 teaspoon salt, and nutmeg to potatoes. Using your hands, gently mix to form a soft but not sticky dough. Transfer dough to a floured surface. Gather into a ball, then divide into 4 pieces.
2Line a rimmed baking sheet with parchment paper; dust with flour. Working with 1 piece at a time (keep other pieces covered with a damp kitchen towel), roll dough into a 24"-long rope. Cut crosswise into 1" pieces. Working with 1 piece at a time, press lightly on gnocchi with the back of the tines of a fork and gently roll gnocchi to create ridges on 1 side. Place on prepared baking sheet and lightly dust with flour. DO AHEAD: Can be made 4 hours ahead. Cover and chill. Cover and chill remaining grated cheese.
3Bring cream, rosemary, and ginger to a boil in a small saucepan. Remove from heat; cover and let steep for 30 minutes. Set aside.
4Preheat oven to 375°F. Bring a large pot of salted water to a boil. Working in batches of about 12 at a time, cook gnocchi until they float to the surface, 2–3 minutes. Using a slotted spoon, transfer gnocchi to a baking dish coated with 1 tablespoon butter.
5Mix 3 tablespoons Parmesan, remaining 1 tablespoon butter, and breadcrumbs in a small bowl. Strain reserved cream mixture into dish all over gnocchi. Break off small pieces of Gorgonzola; scatter over. Sprinkle the remaining Parmesan over, then the breadcrumb mixture.
6Bake until the filling is bubbling and the topping is browned, 25–30 minutes.