How to Make It
Place a pizza stone on the bottom rack of the oven and preheat the oven to 500° for 30 minutes.
Meanwhile, in a small saucepan, combine the butter with 1 tablespoon of water and bring to a simmer. Add the green garlic and cook over moderate heat until softened, about 5 minutes. Add the white wine and cook for 2 minutes. Add the heavy cream and simmer over low heat until reduced by half, about 5 minutes.
On a semolina-dusted work surface, stretch out one of the pieces of dough to a 12-inch round; transfer to a semolina-dusted pizza peel. Spread half of the garlic cream on the dough, leaving a 1-inch border all around. Top with half of the mozzarella and season with salt and pepper. In a medium bowl, use tongs to toss the nettles with the olive oil and season with salt and pepper. Mound half of the nettles on the pizza. Turn on the broiler.
Slide the pizza onto the stone and broil for about 5 minutes, until golden brown and bubbling. Transfer the pizza to a cutting board and garnish with shaved Parmigiano. Repeat to make the second pizza.