Lightly pound pork cutlets between plastic wrap to thin them out and season with salt and pepper. Mix the green olive paste with lime juice and spread each cutlet with some of this mixture. Dip the slices on both sides in bread crumbs, then in egg and in bread crumbs again, making sure all sides are well coated.
With the dull edge of a chef's knife, score the coating in a criss cross pattern and let the slices stand, on a rack, at room temperature for 30 minutes to an hour to let coating set up. (While this is setting up, make your carrot side dish)
In a deep skillet heat 1-inch of vegetable oil to 375 degrees. Deep fry cutlets, olive coated side up, for 2 minutes or until golden brown and cooked through. Remove the meat with a spatula and drain on paper towels.