Lightly beat chicken breast with a meat mallet so the breasts are even in thickness. Season chicken breasts with salt and pepper, to taste.
Create opening in chicken breast to form a pocket. Add two halves of cheese, ham and two more halved slices, tucking ingredients into the pocket. Lightly secure with toothpicks.
Heat oil over medium heat in a large oven-safe skillet. Carefully add chicken and cook 6 minutes on both sides (until chicken is golden and crispy). Remove chicken.
In the same skillet, add butter and garlic. Saute for a minute, stirring frequently. Add flour, mix vigorously. Add chicken broth, lemon juice and lightly season with salt and pepper, mix until everything is incorporated. Simmer another minute until sauce begins to thicken.
Add chicken back to the skillet. Pour sauce over chicken.
Cover skillet with foil and bake 15-20 minutes until chicken is fully cooked.