Set your oven to 430°F (220°C) and grease a baking dish lightly with oil. Presentation starts from here, as the tomatoes and balsamic sauce will form a gorgeous base.
Place the chicken breasts in the prepared baking dish. Drizzle olive oil over them, making sure to coat each side. Sprinkle the oregano, basil, salt, pepper, and half the minced garlic. Rub everything into the chicken for maximum flavor.
Combine balsamic vinegar, the remaining garlic, and brown sugar in a jug or small bowl. Whisk it thoroughly until the sugar dissolves. This balance of sweet and tangy is key to the dish.
Spread the halved grape tomatoes and sliced red onions around the chicken breasts. This adds color, texture, and extra flavor.
Pour the balsamic mixture evenly over the chicken and vegetables. Flip the chicken gently to coat both sides. Bake for 20-25 minutes, depending on the chicken's thickness, until fully cooked.
Once the chicken is cooked through, sprinkle shredded mozzarella over each breast. Place the dish back in the oven under the broiler for 4-5 minutes, or until the cheese is melted and bubbly.
Allow the chicken to rest for 5 minutes before serving. Garnish with freshly chopped parsley or basil for a lovely touch. Enjoy this warm, gooey delight!