Heat olive oil in a cast iron pan or oven-proof skillet over medium low heat. Add shallot and garlic and cook stirring until softened, about 4 minutes. Add spinach and cook until fully wilted. Transfer mixture to a small bowl and give the pan a quick rinse (you'll use it for cooking the chicken).
Combine feta cheese and nutmeg in a medium mixing bowl. Add the spinach mixture and stir until well combined.
Prepare the Chicken
Using a small, sharp knife, carefully cut pockets into the side of each chicken breast.
Sprinkle the salt, pepper and paprika over both sides of the chicken breasts. Rub the seasoning in with your hands.
Divide up the filling and spoon it into the pocket of each breast, packing it in as much as possible as you go.
Cook the chicken
Heat olive oil over medium in the same pan you used for the spinach. Add in the chicken and cook until just browned on each side (about 4 minutes per side).
Place the chicken in the oven and cook for 15-20 minutes (or until it reaches an internal temperature of 165°F).