Preheat & Prep: Preheat your oven to 400°F (200°C). Pat the chicken breasts completely dry using paper towels. Season both sides evenly with sea salt, black pepper, and dried oregano.
Sear (Optional for Maximum Flavor): Heat 1 tablespoon of extra virgin olive oil in a large oven-safe skillet or cast-iron pan over medium-high heat. Sear the chicken for 2–3 minutes on each side until a golden crust forms. Turn off the heat. (Note: If not searing, place the raw seasoned chicken directly into a lightly greased 9x13-inch baking dish).
Toss Tomatoes: In a medium bowl, toss the whole cherry tomatoes and minced garlic with the remaining 1 tablespoon of extra virgin olive oil, a pinch of salt, and a pinch of pepper.
Assemble & Bake: Scatter the seasoned cherry tomatoes and garlic all around the chicken in the skillet or baking dish. Place in the preheated oven and bake for 15–20 minutes, until the tomatoes have softened and burst slightly, and the chicken registers 150°F (65°C) internally.
Add Cheese: Remove the pan carefully from the oven. Place one thick slice of fresh mozzarella cheese directly on top of each chicken breast.
Melt & Broil: Return to the oven and bake for 3–5 minutes until the cheese is completely melted and bubbly. Optional: Switch the oven to broil for the final 60 seconds to get a slightly golden brown cheese topping.
Garnish & Serve: Remove from the oven and let rest for 5 minutes. Garnish generously with fresh basil leaves and drizzle the balsamic glaze over the top. Spoon the warm, garlicky tomato pan juices over the chicken and serve immediately.