How to Make It
Preheat the oven to 375°. On a rimmed baking sheet, bake the potatoes for 1 hour, until tender; let cool slightly. Peel the potatoes and pass them through a ricer into a bowl. Stir in the butter, egg, egg yolk, salt, pepper, nutmeg and 1/2 cup of cheese and let cool.
Lightly dust a baking sheet with flour. Sprinkle the 1 1/4 cups of flour over the potato mixture and gently knead until the flour is almost incorporated. Scrape the dough onto a floured work surface and gently knead until smooth. Divide the dough into 4 equal pieces. Roll out 1 piece of the dough into a 3/4-inch-thick rope. Cut the rope into 1-inch pieces and transfer the gnocchi to the prepared baking sheet. Repeat with the remaining dough. Roll each gnocchi against the tines of a fork or gnocchi paddle to make ridges. Cover the gnocchi with plastic wrap and refrigerate until firm, about 20 minutes.
In a very large skillet, melt 1 tablespoon of the butter in 2 tablespoons of the oil. Add half of the mushrooms and season with salt and pepper. Cook over moderately high heat, stirring, until tender and just browned, about 7 minutes. Add half each of the shallots, garlic and thyme and cook until fragrant, about 3 minutes. Transfer to a bowl. In the skillet, melt the remaining 1 tablespoon of butter in the remaining 2 tablespoons of oil and repeat with the remaining mushrooms, shallots, garlic and thyme. Return all of the mushrooms to the skillet. Stir in the wine and cook until nearly evaporated, about 2 minutes. Add the chicken stock and season the ragù with salt and pepper; keep warm over low heat.
Bring a large pot of salted water to a boil. Add half the gnocchi and simmer over moderately high heat until they rise to the surface, then simmer until cooked through, about 2 minutes longer. Using a slotted spoon, transfer the gnocchi to warm bowls or a platter. Cook the remaining gnocchi. Spoon the ragù over the gnocchi and serve, passing grated cheese at the table.