Preheat oven to 450. Oil a rimmed sheet pan very generously with oil - about 1/4 cup oil.
In a medium bowl, combine ground chicken, grated garlic, breadcrumbs, egg, parmesan, all but 2 tablespoons of the parsley, the zest of the lemon, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Roll mixture into 1-inch round balls and place on prepared sheet pan.
Bake meatballs until well-browned on the bottom and internal temperature is 160, about 10 minutes.
Meanwhile, prepare the sauce. In a large skillet over medium heat, heat 2 tablespoons oil until shimmering. Add sliced garlic and cook until fragrant, about 30 seconds.
Add 1 cup of the chicken stock and bring to a simmer. In a liquid measuring cup, whisk the remaining 1/2 cup chicken stock with the cornstarch until well-combined. When the mixture in the skillet is simmering, add the cornstarch mixture. Cook over medium-low until it starts to thicken, about 5 minutes. A spoon should leave a trail in the sauce for a brief moment.
Add the capers, caper brine, and juice of the lemon and simmer until sauce thickens again, about 2 minutes. Remove from heat.
Add cooked meatballs to the sauce and toss to combine. Add 1/4 teaspoon black pepper and remaining parsley. Serve over something that will soak up the sauce, such as pasta, egg noodles, or mashed potatoes.