Add the parsley, rosemary, garlic, parmesan, olive oil, and bread crumbs to a food processor. Process until a crumbly pesto forms.
Add the pesto to a bowl and the egg to another. Season the lamb steaks with salt and pepper. Dip the steaks in the egg then the pesto to coat, one at a time.
Heat the olive oil in a skillet over medium high heat. Fry the lamb steaks for two minutes or more on each side, depending on the thickness of your steaks and your preferred doneness.