1.Combine steaks and sauces in a large bowl; toss to coat steaks all over in marinade.
2.Meanwhile, peel then grate potatoes coarsely. Using hands, squeeze excess liquid from potato. Spread onto sheets of absorbent paper and squeeze again to remove as much liquid as possible from potato.
3.Heat half of the butter in a large non-stick frying pan. Stir onion over heat until soft. Add potato; stir over heat constantly until potato begins to stick to pan. Remove from heat and cool 5 minutes. Transfer potato mixture to large bowl.
4.Using wet hands, shape potato mixture into eight patties. Heat remaining butter in same pan and in batches, cook hash browns until browned and crisp on both sides. Drain on absorbent paper.
5.Drain steaks; discard marinade. In batches, cook steaks on heated oiled grill plate (or grill or barbecue) until browned on both sides and cooked as desired. Serve steaks with hash browns.