In a medium bowl, whisk together olive oil, white wine vinegar, 3 tablespoons of banana pepper juice, lemon zest, and seasonings.
Place the chicken breasts in a large resealable bag or shallow dish. Pour the marinade over the chicken, ensuring all pieces are well coated. Seal or cover, then refrigerate for at least 2 hours to allow the flavors to meld.
Preheat your oven to 425°F. Line a baking dish with parchment paper or lightly grease it.
Remove the chicken from the refrigerator and discard any remaining marinade. Arrange the chicken breasts in a single layer in the prepared baking dish.
Cover the top of the chicken breasts with as many banana pepper rings as desired. Place the dish in the preheated oven and bake for about 20 minutes, or until the chicken is almost cooked through.
Remove the baking dish from the oven and sprinkle 1 cup of shredded mozzarella cheese evenly over the chicken and peppers. Return the dish to the oven and bake until the cheese is melted and bubbly.