Place whole unpeeled potatoes into a medium saucepan with cold water on medium heat. Bring the potatoes to a boil and cook for 20 to 25 minutes until soft enough to mash. Check with a knife to see if potatoes are cooked through and tender. Once ready drain the potatoes.
When cool enough to handle peel each potato and cut into small pieces and pass them through a potato ricer over a medium size bowl. Add the flour, Parmesan, egg yolks, nutmeg, thyme, salt and pepper and mix into a doughy consistency adding more flour as needed. Transfer dough to a well floured surface.
Using your hands roll pieces of the dough into a rope about 1/2-inch in diameter. With a knife cut the rope into 1/2 to 3/4-inch-long pieces. Flour the pieces as you cut them placing them on a floured baking sheet tray or lined with wax paper. Once rolled you can place the gnocchi in the refrigerator covered with plastic wrap until ready to cook. When ready to cook place gnocchi in boiling salted water for about 1 to 2 minutes. They will rise to the top when done. Using a slotted spoon remove gnocchi from pot.
For the sauce
In a skillet add the butter and mushrooms and saute until nicely browned, about 5 to 7 minutes. Add the white wine and reduce by half, about 5 minutes. Add the cream and gently simmer for another 2 to 5 minutes. Once the sauce has simmered, add the gnocchi and cook for 2 minutes. Garnish with fresh parsley and grated Parmesan.