Place the peeled potatoes in a large pot and cover with cold, salted water. Bring to a boil, then reduce heat and simmer until very tender, about 20-25 minutes. Drain well.

While potatoes boil, melt 1 tbsp of butter in a small skillet. Add the finely minced mushrooms and cook over medium heat until all moisture has evaporated and mushrooms are lightly browned, about 8-10 minutes. Set aside to cool slightly.

Pass the hot, drained potatoes through a potato ricer into a large mixing bowl. If you don't have a ricer, mash them thoroughly with a fork or potato masher until no lumps remain.

Add the remaining 1 tbsp melted butter, cooked mushrooms, egg yolk, salt, and black pepper to the riced potatoes. Gently mix until just combined.

Gradually add the flour, about 1/2 cup at a time, mixing with your hands until a shaggy dough forms. Be careful not to overmix; the less you handle the dough, the lighter the gnocchi will be.

Turn the dough out onto a lightly floured surface. Knead gently for about 1-2 minutes until it just comes together. The dough should be soft but not overly sticky. If too sticky, add a little more flour, a tablespoon at a time.

Divide the dough into 4-6 equal pieces. Roll each piece into a rope about 3/4-inch thick. Cut the ropes into 1-inch pieces.

(Optional) For traditional gnocchi, gently roll each piece over the tines of a fork or a gnocchi board to create ridges. Place finished gnocchi on a lightly floured baking sheet, ensuring they don't touch.

In a large skillet or Dutch oven, melt 2 tbsp butter over medium heat. Add minced garlic and cook for 1 minute until fragrant.

(Optional) Pour in the white wine, if using, and bring to a simmer, scraping up any browned bits from the bottom of the pan. Cook until the wine has reduced by half, about 2-3 minutes.

Stir in the heavy cream and bring to a gentle simmer. Reduce heat to low.

Gradually whisk in the grated Parmesan cheese until smooth and melted. Stir in the freshly grated nutmeg.

Season the sauce with salt and black pepper to taste. Keep warm over very low heat while you cook the gnocchi. If the sauce becomes too thick, add a splash of reserved gnocchi cooking water.

Bring a large pot of heavily salted water to a rolling boil.

Carefully drop the gnocchi into the boiling water in batches. Do not overcrowd the pot.

The gnocchi will sink to the bottom then float to the surface when cooked, typically in 2-3 minutes.

Using a slotted spoon, transfer the cooked gnocchi directly from the boiling water into the skillet with the Parmesan cream sauce.

Gently toss the gnocchi with the sauce to coat evenly. Cook for another 1-2 minutes to allow the flavors to meld. If desired, add a tablespoon or two of gnocchi cooking water to thin the sauce slightly.

Serve immediately, garnished with extra grated Parmesan cheese and fresh chopped parsley.