Preparation of Meatball Mixture: In a large mixing bowl, combine half of the minced shallots with the grated Parmesan cheese, half and half, one third of the bread crumbs, one tablespoon of minced parsley, and the egg. Finely chop one tablespoon of the capers and incorporate them into the mixture. Add the ground chicken to the bowl. Season with kosher salt, black pepper, and garlic powder. Mix gently until all ingredients are thoroughly combined.
Forming the Meatballs: Place the remaining bread crumbs onto a shallow plate. Using your hands, scoop the chicken mixture and shape into twelve uniform meatballs. Roll each meatball in the bread crumbs to coat lightly, aiding in the formation and ensuring each meatball is evenly covered.
Cooking the Meatballs: Heat the olive oil in a large, deep skillet over medium-high heat. Once the oil is hot, add the meatballs. Cook, turning occasionally, until they are browned on all sides, approximately 5 minutes. If necessary, add more olive oil to prevent sticking. Remove the meatballs from the skillet and set them aside on a plate.
Preparing the Sauce: In the same skillet, add the remaining minced shallots and capers. Sauté for approximately one minute, stirring constantly. Deglaze the skillet by adding the white wine and chicken stock. Bring the mixture to a boil, scraping the bottom of the skillet to incorporate any browned bits into the sauce.
Simmering the Meatballs: Return the meatballs to the skillet. Reduce the heat to a simmer and allow the meatballs to cook until the sauce has reduced by half, approximately 6 to 7 minutes. During this time, occasionally stir the sauce to ensure the meatballs are evenly coated.
Finishing the Sauce: Push the meatballs to one side of the skillet. Reduce the heat to very low. Incorporate the fresh lemon juice into the sauce. Gradually whisk in the cold butter cubes, stirring continuously until the sauce is well combined and has slightly thickened. Stir in the remaining tablespoon of parsley. Once incorporated, remove the skillet from heat.
Serving: Toss the meatballs in the sauce to ensure they are well coated. Serve immediately, ensuring each portion is generously covered with the sauce.