Preheat oven to 400°F (200°C).
Pat chicken breasts dry and season generously with salt and pepper.
Heat olive oil in an oven-safe skillet over medium-high heat.
Sear chicken breasts for 2-3 minutes per side until golden brown.
Remove chicken from skillet and set aside.
Add balsamic vinegar, honey or maple syrup, dried basil, dried oregano, and minced garlic to the skillet.
Bring to a simmer and cook for 1-2 minutes, stirring, until slightly thickened to form a glaze.
Return chicken to the skillet, nestling it among the glaze.
Scatter halved cherry tomatoes around the chicken.
Bake for 15-20 minutes, or until chicken is cooked through (internal temperature reaches 165°F/74°C).
Remove skillet from oven and top each chicken breast generously with shredded mozzarella cheese.
Return to oven for an additional 2-3 minutes, or until cheese is melted and bubbly.
Garnish with fresh basil or parsley before serving, if desired.