In a small bowl, combine ricotta, parmesan, basil and garlic.
Rinse chicken and pat dry. Cut a slit along thick edge of each breast half, forming a pocket. Open breast halves like a book and lay one slice of ham in each.
Spoon 1/4 of ricotta mixture on top of each ham slice, then close chicken over filling and fasten with toothpicks.
Season chicken with salt and pepper. Dredge chicken on both sides with flour until well coated. Discard remaining flour.
In a large skillet, warm oil and butter over medium-high heat until butter melts and begins to foam. Add chicken to pan and cook 5 minutes; flip and cook on second side for an additional 4-5 minutes, until chicken is no longer pink inside (cut to test). Serve hot.