In a large bowl, mix together the bread crumbs, milk, and 1 tablespoon wine. Allow this mixture to soak for 5 minutes. Add the chicken, pecorino, egg, parsley, ½ teaspoon of the salt, and the pepper. Using your hands, gently mix together the ingredients until just combined (see Cook’s Note). Refrigerate for at least 2 hours or overnight.

In a medium, straight-sided skillet, add enough olive oil to come 1 inch up the side of the pan. Using a deep-fry thermometer, heat the oil to 350°F.

Working quickly, scoop the mixture into balls, using 2 tablespoons per ball, and gently drop them directly into the hot oil. The meatballs will better retain their shape the colder they are. Fry the balls, rotating often, until they are golden brown all the way around. They will continue to cook when added to the sauce later. Remove to a paper towel–lined tray and set aside.

In another straight-sided skillet, heat 1 tablespoon olive oil over medium-high heat. Add the mushrooms and cook, stirring often with a wooden spoon, until the mushrooms are brown on all sides, about 5 minutes. Add the shallots and remaining ½ teaspoon salt and cook for another 2 minutes.

Reduce the heat to medium and stir in the flour and remaining tablespoon of olive oil to form a paste. Add the 1/3 cup wine and stir until the mixture is smooth. Whisk in the chicken stock and simmer for about 5 minutes.

Add the meatballs to the sauce and simmer for an additional 5 minutes to let the flavors blend and to ensure the meatballs are cooked through. Serve warm garnished with grated pecorino cheese.

Cook’s Note: If you are struggling to get the balls round, it is helpful to pre-scoop the balls onto a parchment-lined tray and place the tray in the freezer for about 15 minutes. Then quickly re-roll the balls to reshape and place them directly into the heated oil.