Mix the Meatballs: In a medium bowl, add the ground chicken, eggs, Italian seasoning, paprika, grated garlic cloves, chopped parsley leaves, lemon zest, chopped capers, parmesan cheese, 1/2 cup of the breadcrumbs, and salt/pepper.Mix to combine. I like using latex gloves on this step, so the mixture is less sticky. Also slightly wetting your hands helps with the mixing and rolling.
Shape the meatballs: Form the chicken mixture into small balls (about 1 heaping tablespoon each). Again gloves or slightly wet hands will make this easier.
Bread the meatballs: Onto a large plate, spread the remaining 1/2 cup breadcrumbs. Roll them in the breadcrumbs to coat.
Sear the meatballs: Into a large nonstick pan set over medium heat, add enough olive oil to coat (about ⅓ cup depending on width of pan). Once the oil begins to shimmer, arrange some of the meatballs in a layer without touching and leaving enough space to turn. Sear, turning until each side is golden brown, about 3 minutes per side. You do not need to fully cook the chicken meatballs at this point, they will finish cooking in the sauce. Transfer to a plate while you work through searing the remaining meatballs.
Make the sauce: Leaving any leftover oil in the pan, add the butter. Stir over medium heat until melted, then add the garlic. Stir until just fragrant, less than one minute, then deglaze the pan with lemon juice and white wine. Use tongs or a non abrasive spoon to scrape any flavorful bits from searing the meatballs stuck to the pan. Add chicken stock and bring to a gentle simmer. If you would prefer a thicker sauce, add a cornstarch slurry (1 tbsp cornstarch mixed with 1 tbsp of water) to the sauce. Add capers and simmer for 5 minutes. Taste and season with salt if desired.
Finish the meatballs: Turn the heat to medium and nestle the meatballs back in the pan. Toss or spoon a bit of the sauce on top. Cover and simmer until the meatballs are cooked through and are no longer pink in the center, about 5 minutes.
Serve: Garnish with chopped parsley, serve hot, with plenty of piccata sauce spooned over top.