Pound chicken breasts to flatten to about 6-8 inches around and about 1/4 inch thick. HINT: I slip them inside a gallon zip freezer bag and then pound them with a rubber mallet, less messy, much easier.
Lay 1 to 2 slices ham over one pounded breast. Try to leave about 1/2-inch margin of chicken breast showing all around...this helps it "seal".
Cut cheese into 4 equal cubes, and place 1 cube of cheese on center of breast/ham combo
Fold sides of breast over to meet in middle and slightly overlap. Then fold ends up toward middle...like you're making a chicken envelope, making certain all ham and cheese is completely encased in chicken.
If you want to cook them right away...secure with toothpicks in middle and on both ends. BUT if you have time...fold up the chicken as described and then wrap it TIGHTLY with plastic wrap (see photo) and chill in fridge for an hour or two (or even overnight). This will mold everything together without the need of toothpicks and makes for a "prettier" end product.
OR...If you'd rather tie it with twine...go for it. I've done it that way too.
Combine coating ingredients in gallon-size zip bag and shake 'em up thoroughly.
If you wrapped your chicken in plastic, remove the plastic wrap now. Dip rolled/stuffed/secured chicken breasts in buttermilk.
Carefully put buttermilk-dipped breast in coating bag and GENTLY coat chicken. Careful, if you used toothpicks they get kind of pokey. Let coated chicken rest for a few minutes (3-5) before frying...this allows the coating to set.
Pan-fry coated chicken breasts in frying pan with 1 inch of oil in bottom...medium heat so oil is about 350-375 degrees. When one side is golden brown, turn it to cook another side (removing toothpicks as you cook so the chicken will sit in the pan). Continue until all sides are golden brown.
Let breasts drain/rest on paper toweling for a few minutes and remove any remaining toothpicks or twine before serving.