Begin by placing a single chicken breast between two sheets of plastic wrap and pounding it delicately but firmly with a rolling pin until it's flattened to an even ¼-inch thickness. Repeat this same process for the remaining piece of chicken.
Now, prepare your ingredients in separate shallow bowls (or plates) - flour, sage leaves, eggs, and breadcrumbs. Dip each chicken roll-up into the flour first, then turn it over and dunk it in the egg mixture, making sure to evenly coat both sides. Finally, press the chicken firmly into the breadcrumbs to bind them together.
Next, place a slice of smoked ham and Emmental cheese atop each piece of chicken. Carefully roll up the breasts, tucking in the ends to secure everything inside. Then, season the outsides of each cordon bleu with salt and pepper for an even more flavorful experience.
Finally, melt a chunk of butter in a large skillet over medium heat and add your chicken roll-ups. Cook them for 3 minutes on each side until they become golden brown on all sides.