Gnocchi is better in a warm cheese bath.
1 teaspoon kosher salt plus more2 tablespoons unsalted butter, room temperature, dividedSpecial EquipmentPlace 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.
Line a rimmed baking sheet with parchment paper; dust with flour. Working with 1 piece at a time , 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:Bring cream, rosemary, and ginger to a boil in a small saucepan.
Preheat 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. Mix 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.