Bring 2 pots, 1 large and 1 medium, with well-salted water to a boil over medium heat. Set up a bowl of well-salted ice water. Blanch the fresh peas in the medium pot of boiling water until they are cooked but still crunchy and then immediately plunge them into the salted ice water. Remove them from the ice water and reserve.
Coat a large saute pan over medium heat with olive oil. Add the smashed garlic cloves and crushed red pepper. Bring the pan to a medium high heat. When the garlic has become golden brown and is very aromatic, remove it and discard. Add the prosciutto and saute until it starts to get crispy, 1 to 2 minutes. Add the mushrooms and season with salt. Saute for 3 to 4 minutes, and TASTE to see if they are delicious (they should be!).
Add the peas and chicken stock. Season with salt, TASTE IT (it should be more delicious). Simmer until the stock has reduced by about half.
While the stock is reducing, add the gnocchi to the large pot of salted boiling water. Cook the gnocchi until they float and get very puffy. The gnocchi should be really puffy.
While the gnocchi is in the boiling water, add the butter to the pan with the mushroom mixture. Cook over low heat and swirl to incorporate. TASTE and adjust seasoning if needed.
When the gnocchi are cooked, carefully remove them from the cooking water and add them to the pan with the mushrooms. Toss or stir to combine. Cook the gnocchi with mushroom mixture until it clings to the gnocchi. Add the grated Parmigiano and the chopped chives. Transfer to serving bowls and serve immediately.
Call yourself a superstar!
Preheat the oven to 375 or 400 degrees F.
Bake the potatoes until they are fork tender, about 45 minutes to 1 hour. Check them!
While the potatoes are still hot peel and pass them through a food mill or ricer. (I find that the food mill works just as well as a ricer and is much easier to handle) onto a sheet tray lined with parchment paper. When doing this pay careful attention to keep the potatoes as light and fluffy as possible. This will aid in keeping the gnocchi light. Refrigerate the potatoes on the sheet tray until cold. This is also a very important step. If the potatoes are warm while adding flour they will require more flour which will result in a much heavier finished product.
When the potatoes are absolutely cold, transfer to a clean work surface. Beat together the eggs and cheese and pour onto the potatoes. Season with salt. Cover generously with flour. It should look like snow on the mountains.
Crumble the potato flour mixture between your fingers. Begin to knead the dough until it is a dry homogeneous mixture. The dough should feel slightly moist, but not tacky. If too tacky, repeat the snow on the mountains stage.
Form the dough into a large log. Cut slices off the log and begin to roll into long ropes that are about 1-inch in thickness. Cut the ropes into 1/2-inch lengths. Cover generously with flour. Place the gnocchi in a single layer on a sheet tray dusted with flour. DO NOT PILE ON TOP OF EACH OTHER!!
Use or freeze the gnocchi immediately. If freezing, place tray directly into the freezer. Once frozen, the gnocchi can be stored in plastic bags, in the freezer, indefinitely. When cooking gnocchi they can go directly from the freezer into salted boiling water.
Note: It is a general practice to take gnocchi out of the water when they float. This is a big mistake. Gnocchi need to be cooked in boiling water until they float and get nice and puffy. Not cooking gnocchi long enough will also result in heavy gnocchi.
P.S. These are Chef Anne "Secrets" to great gnocchi, use them and you will be successful every time.