Lay the thighs out on a plastic cutting board and cover them in plastic wrap. Beat them with a rolling pin or a skillet, until slightly flattened. Sprinkle them with salt.
Place two pieces of ham over the chicken. Place one piece of cheese on each end and roll the thighs up into a roulade.
Coat the chicken rolls in flour, then the egg, then the crumbs, be sure to coat evenly in each stage.
Heat an oven proof skillet to medium heat and add the oil. Once hot, carefully place the chicken rolls, seam side down, into the skillet. Let brown, then turn over. Brown several more minutes, then place the skillet in the oven for 20 minutes.
Remove from heat. Let the chicken rest about 5 minutes before serving.