Preheat your oven to 400°F (200°C). In a large bowl, place the chicken thighs and season generously with the dried oregano, dried basil, salt, and ground black pepper. Toss everything together so the chicken is well coated with the herbs and seasoning.
Heat a large oven-safe skillet over medium-high heat. Add the olive oil and swirl to coat the bottom of the skillet. Add the seasoned chicken thighs from Step 1 and sear them for 3 to 5 minutes on each side, or until the chicken is golden brown.
Add 1 cup of the halved grape or cherry tomatoes into the skillet around the browned chicken. Transfer the skillet to the preheated oven. Bake for about 20 minutes, or until the chicken is cooked through and has reached an internal temperature of 165°F (74°C).
Remove the skillet from the oven. Carefully top each piece of chicken with slices of fresh mozzarella. Set your oven to broil and return the skillet to the oven for 2-3 minutes, or until the cheese is fully melted and bubbly. I like to keep a close eye while broiling to make sure the cheese doesn't burn.
Serve the cheesy baked chicken immediately, drizzling generously with balsamic glaze and garnishing with chopped fresh basil. If you like, add extra halved cherry tomatoes for a fresher finish. This final touch really brightens up the dish!