Pat the chicken breasts dry with paper towels and season both sides generously with salt and pepper.
Using a sharp knife, carefully cut a horizontal pocket into the thick side of each breast, making sure not to cut all the way through.
Mix chopped herbs, lemon zest or juice, and minced garlic, then stuff this mixture along with cheese and spinach into each pocket, filling generously.
Heat a tablespoon of olive oil in a skillet over medium-high heat until shimmering and fragrant.
Place the stuffed chicken breasts seam-side down into the hot skillet and cook for about 6-7 minutes until golden brown and crispy on the bottom.
Turn the chicken breasts with tongs and cook for another 6-7 minutes, ensuring even browning.
Use an instant-read thermometer to check that the internal temperature reaches 74°C (165°F). Remove from heat once done.
Transfer the chicken to a plate, tent loosely with foil, and let rest for 5 minutes to retain juices.
Slice the chicken crosswise to reveal the juicy, flavorful filling inside, and serve hot.