Trim the pork tenderloin of excess fat and silver skin. Cut crosswise into 4 even pieces. Cut each piece crosswise again, but do not go all the way through; you should be able to open it like a book. Pound each piece with a mallet until 1/4-inch thick and 6 to 8 inches across.
Whisk together the buttermilk, salt, black pepper, garlic powder, onion powder, paprika and sugar in a shallow dish. Add the pork cutlets. Make sure all the pieces are coated well with the buttermilk marinade. Cover and keep refrigerated for at least 4 hours and up to overnight.
Heat 1/2-inch oil in a large high-sided skillet to 350 degrees F. Set up a breading station of three shallow dishes consisting of the flour in the first dish, eggs in the second and breadcrumbs in the third. Sprinkle all three dishes with salt and pepper.
Dredge each cutlet in the flour first, then in the egg and finally in the breadcrumbs. Gently place into the hot oil without overcrowding the skillet. You will need to fry the cutlets in batches. When the cutlets are golden brown on one side, about 2 minutes, carefully flip and cook for another 2 minutes. Drain well on a paper-towel-lined plate.
Build the sandwiches by putting the cutlets between the burger buns and garnishing with lettuce, tomato, onion, pickle, mayonnaise and mustard. The cutlet should hang generously over the bun.