Preheat the oven to 375°F (190°C).

In a small mixing bowl, combine the crumbled feta cheese, chopped spinach, minced garlic, and dried oregano until well integrated.

Place each chicken breast on a cutting board and slice a pocket into the thickest part of the side, taking care not to cut all the way through.

Stuff each chicken pocket evenly with the feta and spinach mixture; secure the openings with wooden toothpicks if necessary.

Season the exterior of the chicken breasts evenly with kosher salt and black pepper.

Heat olive oil in a large oven-safe skillet over medium-high heat on the stovetop.

Place the chicken in the skillet and sear for 3 to 4 minutes per side until a golden-brown crust has formed.

Transfer the skillet directly into the preheated oven and bake for 12 to 15 minutes, or until the internal temperature reaches 165°F (74°C).

While the chicken is baking, combine the balsamic vinegar and honey in a small saucepan over medium heat; simmer until reduced by half and slightly thickened.

Remove the chicken from the oven, let rest for 5 minutes, and drizzle with the balsamic glaze immediately before serving.