Start by preheating your oven to 400°F, then place your chicken breasts on a clean cutting board. Using a sharp knife, carefully make five parallel slits in each breast, spacing them about half an inch apart. The trick is cutting about three-quarters of the way through the chicken without breaking through the bottom. This creates pockets that will hold all your delicious fillings while keeping the chicken intact during cooking.
In a small bowl, whisk together the olive oil, fresh lemon juice, chopped dill, chopped parsley, and minced garlic until well combined. This fragrant mixture will infuse the chicken with incredible Mediterranean flavors and help keep it moist during baking. Drizzle this mixture over the chicken breasts, making sure to work some of it into each slit with your fingers or a small spoon.
Season the chicken generously with kosher salt and freshly ground black pepper, both on top and in the slits. Now comes the fun part - stuffing each breast with your prepared vegetables. Alternate between zucchini slices, tomato slices, red onion pieces, and thin lemon slices, creating beautiful layers in each pocket. The vegetables should fit snugly but not be packed too tightly.
Sprinkle the crumbled feta evenly over the top of each stuffed chicken breast, followed by the shredded mozzarella. The combination of these two cheeses creates the perfect balance of tangy and creamy flavors that will melt beautifully during baking. Don't worry if some cheese falls onto the baking sheet - it will create delicious crispy bits.
Place the baking sheet in your preheated oven and bake for about 25 minutes, or until the chicken reaches an internal temperature of 165°F and is no longer pink inside. The cheese should be golden and bubbly, and the vegetables should be tender. Let the chicken rest for 5 minutes before serving to allow the juices to redistribute.