Preheat the oven to 400°F.

Place the potatoes directly on the oven rack with a baking sheet underneath. Sprinkle with kosher salt and rub the potatoes evenly with olive oil.

Bake for 50 to 60 minutes, until completely tender when pierced with a knife.

Let the potatoes cool just until you can comfortably handle them. They should still be warm.

Peel the potatoes and pass them through a ricer or food mill onto a clean work surface.

Sprinkle 1 cup of flour and the remaining ½ teaspoon kosher salt over the potatoes. Gently mix to combine.

Add the egg and gently work the dough together with your hands, adding more flour as needed until the dough is soft, cohesive, and slightly tacky but not sticky. Avoid overworking.

Divide the dough into 3 portions. Roll each portion into a rope about ¾ inch thick.

Cut into bite-size pieces. Lightly pinch each piece to create a small indentation in the center if desired.

Transfer the gnocchi to a floured baking sheet and refrigerate while you prepare the sauce.

Heat olive oil in a large skillet over medium-high heat. Add the shallot and cook for about 1 minute, until softened.

Add the mushrooms and cook for 8 to 10 minutes, stirring occasionally, until they release their moisture and begin to brown.

Stir in the garlic, thyme, and butter if using. Cook for 30 seconds, until fragrant.

Deglaze the pan with the white wine and simmer for 2 to 3 minutes, until reduced by about half.

Lower the heat to medium-low. Add the heavy cream and simmer until slightly thickened.

Season with salt and black pepper.

Add the chopped chestnuts.

For softer chestnuts, add them before the cream and let them simmer longer.

Bring a large pot of water to a boil and season with kosher salt.

Cook the gnocchi in batches. They are done 1 to 2 minutes after they float to the surface. Reserve 1 cup of the cooking water.

In a large sauté pan, heat olive oil and butter over medium heat. Add the cooked gnocchi and cook, stirring gently, until lightly golden on all sides.

Add the gnocchi to the sauce and toss to coat. Stir in the grated Parmigiano Reggiano, then gradually add reserved gnocchi cooking water as needed until the sauce is smooth, creamy, and coats the gnocchi evenly.

Serve hot, garnished with chopped parsley, Parmesan shavings, and freshly ground black pepper.