In a heavy bottomed saucepan, combine balsamic vinegar, garlic, bay leaf, & honey. Stir with a wooden spoon until honey has dissolved. Bring to a simmer over medium heat, turn heat down to medium-low and continue to simmer, stirring occasionally, until it becomes syrupy and coats the back of a spoon, about 12-15 minutes. Watch closely so it doesn’t burn. Keep warm enough to pour until needed. (Remember to remove the bay leaf before serving.)
Preheat grill on medium heat for 30 minutes. Brush chicken breasts evenly with olive oil, and season with kosher salt & fresh ground black pepper. Place the chicken breasts evenly over the hot grill. Every 3 minutes turn each breast 90 degrees, and flip when needed. Once the chicken breast reaches 165 degrees internal temperature, it is fully cooked. Place chicken on cutting board and let rest 5 minutes. While chicken is resting, brush peaches with a little olive oil. Place peaches, cut side down, on grill. Grill for about 3 minutes, total time, turning to achieve grill marks on all cut sides. Remove from grill and let cool to room temperature.
On each plate place one chicken breast, then grilled peaches, tomatoes, basil leaves & burrata cheese, divided evenly. Season lightly with kosher salt & fresh ground black pepper. Drizzle 1-2 tbsp. of the balsamic reduction over salad. Serve & Enjoy!