Place chicken breasts on a flat work surface. Slice each horizontally through the middle, being careful not to cut all the way through to the other side. Open the 2 sides and spread them out like an open book. Place each one between 2 sheets of heavy plastic. Firmly pound chicken with the smooth side of a meat mallet to a 1/4-inch thickness.
Preheat the oven to 375 degrees F (190 degrees C).
Season insides of chicken with salt, pepper, and garlic powder. Layer spinach, tomato, onion, and feta cheese over chicken in that order. Roll chicken over the stuffing and tie ends with butcher's twine.
Mix olive oil, lemon juice, garlic, oregano, rosemary, thyme, salt, and pepper together to make the sauce.
Heat a cast iron skillet over high heat. Add chicken; cook until browned, about 5 minutes per side. Brush 1/2 of the sauce on top.
Bake in the preheated oven for 30 minutes. Pour the remaining sauce over chicken. Continue baking until an instant-read thermometer inserted into the center reads at least 165 degrees F (74 degrees C), 10 to 15 minutes more.
Remove chicken and let rest for 5 minutes. Slice into pinwheels and serve with pan juices.