Heat the oven to 375°F. Oil a 9-by-5-inch metal loaf pan and line with a parchment sling. Soak potato bread crumbs in milk for 5 minutes.
Stir eggs, pickles, onion, Worcestershire, salt and pepper into the crumbs. Fold in beef and cheddar cubes just until distributed.
Transfer to the loaf pan and level gently. Bake for 40 minutes.
Mix mustard and pickle brine and brush over the top. Bake for 15 to 25 minutes more until the meat in the center reaches 160°F, checking away from a cheese pocket.
Rest in the pan for 15 minutes. Lift with the parchment sling and allow excess juices to drain.
Cut into 8 slices with a sharp knife, supporting the cheese-filled slices with a spatula.