Add half of shallots to a large bowl. Stir in Parmesan cheese, half and half, 1/3 cup bread crumbs, 1 tablespoon parsley, and egg. Roughly chop 1 tablespoon capers and add to the bowl; add ground chicken. Season with salt, pepper, and garlic powder. Mix gently together until everything is well incorporated.

Add remaining bread crumbs to a work surface or shallow dish.  Form chicken mixture into 12 meatballs, rolling each one lightly in bread crumbs to coat and to help shape the meatballs.  

Heat oil in a large deep skillet over medium-high heat. Add meatballs to skillet and cook, turning occasionally, until browned on all sides, about 5 minutes, adding more oil if necessary. Remove meatballs from skillet and set aside.

Add remaining shallot and capers to the skillet and cook stirring constantly, for 1 minute.  Pour in wine and stock and bring to a boil. Return meatballs to the skillet, reduce heat, and simmer until liquid is reduced by half, stirring occasionally, to coat meatballs in the sauce, 6 to 7 minutes.

Once sauce is reduced, move meatballs to one side of the skillet and turn the heat to very low. Whisk in lemon juice and cold butter, stirring constantly, until well incorporated and slightly thickened. Stir in parsley and pepper and remove from heat. Toss meatballs well with sauce and serve immediately.