How to Make It
In a large bowl, combine the Parmesan with the 1 cup of Pecorino, the bread crumbs, parsley, eggs and half of the garlic and stir until a soft dough forms. Using moistened hands, roll the mixture into 3/4-inch balls and arrange in a single layer on a baking sheet lined with plastic wrap. Refrigerate until chilled and firm, about 30 minutes.
Meanwhile, in a medium saucepan, heat the olive oil until shimmering. Add the remaining garlic and cook over moderately high heat until softened, about 30 seconds. Add the greens and cook, stirring, until wilted and just beginning to brown, 3 to 4 minutes longer. Add the stock and bring to a simmer. Drop the dumplings into the simmering stock and cook until they rise to the surface, about 5 minutes. Season the soup with salt and pepper and serve in deep bowls, passing extra Pecorino at the table.