Preheat your oven to 375°F (190°C).
In a skillet over medium heat, heat olive oil and sauté the onions until translucent, about 5 minutes.
Add garlic and chopped spinach to the onions, cooking until the spinach is wilted, about 2-3 minutes.
Remove the skillet from heat and mix in the crumbled feta and oregano; season with salt and pepper.
Butterfly the chicken breasts and pound them to an even thickness for uniform cooking.
Spread the feta and spinach mixture evenly over each chicken breast, then roll them up tightly and secure with toothpicks or kitchen twine.
Season the outside of the rolled chicken with salt and pepper, then place in a baking dish.
Pour chicken broth into the bottom of the baking dish to keep the chicken moist while cooking.
Bake in the preheated oven for 25-30 minutes, or until the chicken is cooked through and reaches an internal temperature of 165°F (74°C).
Let the chicken rest for 5 minutes before slicing to retain its juices.
