Preheat oven to 450°F. Coat a large rimmed baking sheet with cooking spray.

To prepare meatballs: Place ground chicken, egg, panko, Parmesan, 2 cloves minced garlic, lemon zest, parsley, salt and pepper in a large bowl. With clean, wet hands, gently mix to thoroughly combine. Form into 16 meatballs (generous 2 tablespoons each) and place on the prepared baking sheet. Bake until an instant-read thermometer inserted in the center registers 165°F, about 15 minutes.

Meanwhile, make sauce: Heat oil in a medium saucepan over medium heat. Add shallot; cook, stirring, until softened, about 2 minutes. Add garlic; cook, stirring, until fragrant, about 1 minute. Sprinkle with flour; cook, stirring, for 1 minute. Stir in broth and wine; simmer until thickened and reduced by about half, 5 minutes. Remove from heat and stir in lemon juice, butter and capers.

Serve the meatballs with the sauce. Garnish with parsley, if desired.