Preheat oven to 425 degrees F.
If pieces of chicken are very thick, lightly pound with a mallet to even thickness.
Using a sharp knife, hold the chicken breast steady with one hand and carefully make a horizontal cut along the thicker side, parallel to the cutting board, almost to the other side, but leaving about a half-inch border to keep the pocket intact. Be careful not to slice all the way through. Gently open up the pocket, being careful not to tear the edges, creating a pocket where you can stuff the filling. Repeat this process with the remaining pieces of chicken.
Place the shredded zucchini between a double layer of paper towels and holding it over a sink, squeeze out as much liquid as possible. Transfer the zucchini to a medium bowl and combine with the feta, cream cheese, garlic, salt, and pepper.
Divide the zucchini mixture evenly between the pockets of the chicken breasts. Use 2 or 3 toothpicks per piece of chicken to help secure the edges and help prevent the filling from spilling out, if desired.
Line a rimmed baking sheet with parchment paper and preheat oven to 425 degrees F.
In a small bowl, combine the Italian seasoning, granulated garlic (or garlic powder), smoked paprika, and salt. Season both sides of each piece of stuffed chicken with the spice mixture and set aside.
Heat 2 tablespoons oil in a large skillet over MEDIUM heat. Sear the chicken, in batches, for about 2 to 3 minutes per side. Use tongs to carefully flip the chicken and cook until browned on both sides.
Transfer the seared chicken to the prepared baking sheet and transfer it to the preheated oven. Cook for 20 to 22 minutes, or until the internal temperature of the chicken reaches 165 degrees F.
Remove from the oven and let rest for 5 minutes. Remove the toothpicks and serve.