Cooking Steps
In a large bowl, combine chicken, bread crumbs, finely grated Parmesan, lightly beaten large egg, 2 finely chopped cloves garlic, and 2 tbsp. chopped fresh parsley. Season with kosher salt and a few grinds of black pepper.
Form mixture into 12 meatballs (about 3 tablespoons each). If mixture is too sticky, slightly wet your hands to help form balls.
In a large, high-sided skillet over medium heat, heat oil. Add meatballs and cook, turning occasionally, until golden brown on all sides and almost cooked through, 10 to 12 minutes. Transfer to a plate.
In same skillet over medium heat, melt butter.
Add finely chopped small shallot and 2 finely chopped cloves garlic, and cook, stirring occasionally, until softened and translucent, about 5 minutes.
Add tomato paste and cook, stirring frequently, until darkened and fragrant, about 3 minutes.
Add vodka and cook, stirring, until evaporated, about 1 minute more.
Slowly add heavy cream and water. Stir until smooth, then stir in crushed red pepper flakes. Season with kosher salt and black pepper.
Return meatballs to skillet and reduce heat to low. Turn meatballs to coat in sauce.
Cover skillet and cook, stirring occasionally and adding more water if sauce is too thick, until meatballs are cooked through, 8 to 10 minutes.
Add finely grated Parmesan and stir until melted.
Transfer meatballs to a platter. Top with more grated Parmesan and chopped fresh parsley before serving.
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