Set three wide, shallow dishes (such as pie plates) in a row on the counter. Put the flour in the first dish. Crack the egg into the second dish and beat it lightly with a fork. Put the panko or crumbs in the third dish and toss them with 1/2 tsp. salt and 1/4 tsp. pepper.
Working with one slice at a time, dredge the meatloaf first in the flour and then in the egg, coating it on all sides and shaking gently after each dip to knock off the excess. Lay the meatloaf in the crumbs, scatter some crumbs on top of the slice, and press gently to adhere. Flip and repeat once or twice with the crumbs to coat really well; be sure to get the edges as well. As you finish each slice, set it on a tray. When all are coated, refrigerate for at least 5 minutes and up to 1/2 hour to let the breading set up. Save some of the leftover crumbs for testing the frying oil temperature and discard the remaining breading ingredients.
When ready to cook, pour about 1/3 inch of oil into a heavy-duty 10-inch straight-sided sauté pan. Have ready a paper-towel-lined tray or plate. Heat the oil over medium-high heat until it immediately and vigorously bubbles when you gently flick a few leftover crumbs into it.
With a slotted metal spatula, carefully slip the breaded meatloaf into the oil. Fry until golden brown on both sides, about 1 minute per side, using the spatula to carefully turn the slices. Transfer to the paper towels, sprinkle lightly with salt, and let sit briefly to drain excess oil. Serve hot.