Boil the potatoes: Place potatoes in a large pot, cover with cold water, and add a generous pinch of salt. Bring to a boil, then reduce heat and simmer until very tender when pierced with a fork, about 20-25 minutes. Drain well and let cool slightly.

Cook the mushrooms for gnocchi: While potatoes cook, heat 1 tbsp olive oil in a skillet over medium-high heat. Add finely chopped cremini mushrooms, salt, and pepper. Sauté until all liquid has evaporated and mushrooms are deeply browned and tender, about 8-10 minutes. Set aside to cool.

Rice the potatoes: Peel the slightly cooled potatoes. Pass them through a potato ricer directly onto a clean, dry surface or into a large mixing bowl. If you don't have a ricer, mash them thoroughly with a fork or masher until no lumps remain. Spread them out to allow steam to escape for a few minutes.

Form the dough: Create a well in the center of the riced potatoes. Add the cooled sautéed mushrooms, egg yolk, 1/4 cup grated Parmesan, and 1/2 tsp salt. Gradually add 1 1/2 cups flour, gently incorporating with your hands or a fork until a soft, slightly sticky dough forms. Be careful not to overwork the dough, as this can make the gnocchi tough.

Shape the gnocchi: Lightly dust your work surface with flour. Take a portion of the dough (about a tennis ball size) and gently roll it into a long rope, about 1/2 to 3/4 inch thick. Cut the rope into 3/4-inch pieces. You can leave them as is or gently roll each piece against the tines of a fork or a gnocchi board to create ridges (this helps sauce adhere). Place formed gnocchi on a lightly floured baking sheet, ensuring they don't touch. Repeat with the remaining dough.

Heat 2 tbsp olive oil in a large skillet over medium-high heat. Add sliced mixed mushrooms and sauté until browned and tender, about 5-7 minutes.

Add minced garlic and cook for another minute until fragrant. Stir in chopped fresh parsley. Season with salt and black pepper to taste. Remove from heat and set aside.

Melt 4 tbsp unsalted butter in a large, deep skillet or Dutch oven over medium heat. Add minced garlic and cook until fragrant, about 30 seconds to 1 minute, being careful not to burn it.

If using, pour in white wine and bring to a simmer, scraping up any browned bits from the bottom of the pan. Let it reduce by half, about 2-3 minutes.

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

Gradually whisk in 1 cup grated Parmesan cheese until smooth and melted. Stir in freshly grated nutmeg. Season with salt and black pepper to taste. Keep warm over very low heat.

Boil the gnocchi: Bring a large pot of generously salted water to a rolling boil. Carefully add the gnocchi in batches (do not overcrowd the pot). They will sink initially, then float to the surface when cooked, usually within 2-3 minutes.

Sear the gnocchi (optional, but recommended): Using a slotted spoon, transfer the cooked gnocchi directly into the Parmesan cream sauce. Alternatively, for extra texture, you can pan-fry the cooked gnocchi after boiling. Heat 1 tbsp olive oil or butter in a separate skillet over medium-high heat. Add the cooked gnocchi in a single layer and sear until lightly golden and slightly crispy on the outside, about 2-3 minutes per side. Then, add them to the cream sauce.

Combine and serve: Gently toss the gnocchi in the Parmesan cream sauce until well coated.

Serve immediately, topped with the sautéed mixed mushrooms. Garnish with extra grated Parmesan cheese and fresh parsley, if desired.