Optional: To make homemade balsamic glaze, bring ½ cup balsamic vinegar to a boil in a small saucepan over medium-high heat. Reduce the heat to low and simmer, stirring occasionally, until reduced by half (10–15 minutes). Let it cool—this step can be done up to 4 days ahead.
Prepare the marinade by whisking together olive oil, balsamic vinegar, Italian seasoning, honey, salt, and pepper in a large shallow dish. Add the chicken, turning to coat both sides, then cover and marinate for 30 minutes to 8 hours in the refrigerator.
Preheat your grill (or grill pan) to medium-high heat, about 400°F. Remove the chicken from the marinade, allowing excess to drip off, and discard used marinade. Grill the chicken for 5–6 minutes per side, or until the thickest part reaches 165°F. Let rest briefly.
While the chicken is cooking, combine halved cherry tomatoes, olive oil, and a pinch of salt in a bowl. Gently fold in fresh basil just before serving to keep the herbs bright and fresh.
Plate each grilled chicken breast and top with burrata (quartered or halved), a generous serving of tomato-basil salad, and a drizzle of balsamic glaze. Finish with flaky sea salt and fresh black pepper. Serve immediately and enjoy!