Place the chicken breasts between two sheets of plastic wrap and gently pound them with a meat tenderizer or rolling pin until they are about ¾ inch thick throughout. This ensures even cooking and juicy results. Season both sides generously with salt and black pepper.

In a medium bowl, whisk together the balsamic vinegar, honey (or brown sugar/maple syrup), minced garlic, Dijon mustard, and dried oregano or rosemary.

Pour half of the marinade over the seasoned chicken breasts and let them marinate for 15-30 minutes if time allows. Reserve the remaining sauce for glazing later. If short on time, brush the marinade directly onto the chicken.

Preheat the oven to 400°F. Lightly oil a baking dish or foil-lined sheet pan. Arrange the marinated chicken breasts in a single layer. If using cherry tomatoes, scatter them around the chicken.

Place the pan in the oven and bake at 400°F for 18-22 minutes, or until an instant-read thermometer inserted into the thickest part of the chicken reaches 165°F.

While the chicken bakes, pour the reserved marinade into a small saucepan. Bring it to a boil over medium-high heat, then reduce to low and simmer for 5-8 minutes, stirring occasionally, until thickened slightly.

Remove the chicken from the oven. If adding mozzarella, sprinkle it over the chicken and return to the oven for 2 minutes until melted. Brush the thickened glaze over the chicken and let it rest for 5 minutes before slicing to allow juices to redistribute.