Preheat oven to 375 F.
Wrap your chicken breasts loosely in plastic wrap. You want it loose enough that they'll be able to comfortably expand, but not too loose that they're "expand" in little pieces all over your kitchen when you smack the crap out of them.
Take a meat mallet or bottom side of a pan and get to smacking. Flatten the breasts to about 1/4 to 1/2 inch thickness.
Remove plastic wrap from chicken breasts.
Place a piece of country ham on chicken breast.
Place a piece of manchego cheese on top of country ham.
Using butcher's twine or toothpicks (these are more ideal), wrap the chicken breast around the ham and cheese. If I had toothpicks handy, I would have used those, but the twine sufficed.
Place the flour in a shallow dish. Season with salt and pepper. Dredge the chicken in the flour, shaking off any excess flour.
Heat the oil in an oven-proof skillet under medium high heat. Place the chicken in the pan, seam-side up. Cook chicken until you get a nice golden crust, about 3-4 minutes. Flip chicken over and cook for an additional minute.
Transfer chicken to the oven to finish, about 10 minutes or until internal temperature reaches 165F.
Serve chicken with barbecue sauce (or sauce of your choice) and side of your choice. We paired this with macaroni and cheese for a nice comforting meal!