For the gnocchi: In a large stock pot over high heat, boil the potatoes, salt, smashed garlic, and roughly chopped onions until the potatoes are fork tender, 10 to 12 minutes. Drain and return to the pot to allow the water to cook off, 5 to 10 minutes.
Meanwhile, in a small saute pan over medium-high heat, add the olive oil and heat until shimmering. Add the diced onion and cook for 3 to 4 minutes. Add the minced garlic and saute for 1 minute more. Add the spinach and cook for 3 minutes. Add the wine and cook until the spinach is wilted, 5 minutes, stirring often. Place the mixture in a strainer set over a bowl to catch the liquids as it drains off, applying pressure gently a few times to accelerate liquid removal. Reserve 1/2 cup liquid.
When the potatoes are dry and slightly cooled, roughly cut them and pass through a food mill or ricer. Set aside. (Guy's tip: after ricing the potatoes, spread them out on a baking sheet and allow them to dry out even more to remove moisture).
In a food processor bowl fitted with the bottom blade, add the strained spinach, pulse to puree, and then add the egg and egg yolk, flour, nutmeg, and Parmesan. Pulse until well mixed. Place into a large bowl and gently fold in the riced potatoes, gently stirring until just combined. You will have very soft dough. Turn out onto a lightly floured board and roll into a 1 1/2-inch thick snake. Dust the dough lightly with flour and cut into 1 1/2-inch pieces. Roll each piece gently with your thumb, leaving a small indentation on 1 side of the gnocchi. Place the finished gnocchi on a lightly floured, parchment paper-lined baking sheet. (Guy's tip: if you have time, let the gnocchi rest in the refrigerator or freezer until chilled prior to cooking. It will help the gnocchi hold its shape better).
Fill a large stock pot 3/4 full with water, place over high heat, add 1 tablespoon kosher salt, and bring to a rapid boil.
Meanwhile, for the sauce: Wipe clean the same pan that the spinach was cooked in and place over medium-high heat. Add 3 tablespoons butter and melt. Add the garlic and chile flakes and cook for 1 to 2 minutes. Deglaze with the wine, reduce for 4 to 5 minutes. Add the stock, reserved spinach liquid, half-and-half, and cheese and reduce an additional 3 minutes. Add the pepper, tomatoes, and remaining 2 tablespoons butter.
When the sauce is ready, add the gnocchi to the boiling water and cook for 3 1/2 minutes. Remove, drain, and let rest for 5 minutes. Add to the sauce and garnish with Parmesan and a drizzle of extra-virgin olive oil. Freeze any leftover gnocchi for a later meal.