Add grated garlic, one-third of the grated hard cheese, egg, bread crumbs, Provencal herbs, salt, and ground black pepper to the minced chicken. Mix until well combined.
Divide the minced chicken mixture into 16-18 pieces. Cut the remaining hard cheese into 16-18 cubes. Form each piece of minced chicken into a ball, insert a cheese cube into the center, pinch to seal, and shape into a round meatball.
Dip each meatball in flour to coat completely.
Heat vegetable oil in a frying pan over medium heat. Fry the meatballs, turning occasionally, until golden brown on all sides, about 8-10 minutes.
Grease a baking sheet with vegetable oil. Transfer the fried meatballs to the prepared sheet. Bake in a preheated oven at 180°C (356°F) for 20-30 minutes until the internal temperature reaches 74°C (165°F).
Grate the onion and remaining garlic cloves. Heat olive oil in a skillet over medium heat. Add the grated onion and garlic, stirring occasionally, and cook for 5 minutes. Add Provencal herbs and cook for 1 minute, stirring.
Add the canned tomatoes and their juice to the skillet.
Bring the sauce to a boil, then reduce heat to low, cover, and simmer for 10 minutes. Add salt and sugar to taste.
Serve the baked chicken meatballs with the tomato sauce.