Stir together breadcrumbs and milk in a large bowl; let sit until absorbed, about 10 minutes. Add egg and beat lightly into breadcrumbs with a fork. Add Parmigiano-Reggiano, ricotta, onion, grated garlic, Italian seasoning, salt, and pepper; stir to combine. Add chicken and mix gently with a fork until incorporated (do not overmix). Refrigerate until chilled and easy to handle; about 30 minutes. (If the mixture is still too soft to handle, chill for an additional 10 minutes before shaping.) Roll meatballs into 1 ½-inch balls (1 ½ oz. each) and place on a parchment lined baking sheet.

Heat 2 tablespoons oil in a large nonstick over medium heat. Working in two batches and keeping the remaining batch chilled, add about 15 meatballs to skillet and cook, turning occasionally, until browned on all sides and an instant-read thermometer registers 160°F, about 10 minutes. Transfer meatballs to a shallow bowl and cover with foil to keep warm. Repeat with remaining oil and meatballs. Do not wipe skillet clean.

Add garlic; cook over medium, stirring constantly, until fragrant and lightly golden brown, 20 to 30 seconds. Pour chicken stock into skillet, scraping up any browned bits from bottom of skillet using a wooden spoon. Cook, stirring occasionally, until liquid is slightly reduced, about 3 minutes.

Add butter, 1 piece at a time, and stir until completely melted before adding next piece. Immediately remove skillet from heat. Divide meatballs among 4 shallow bowls and top with about 3 tablespoons of the garlic-butter sauce. Garnish with parsley and serve immediately with lemon wedges.