In a medium skillet over medium heat combine 2 tablespoons oil and 2 tablespoons butter. When butter melts into oil add hash browns and thinly sliced onions, season with salt and pepper. Cook 7 to 8 minutes, turn with spatula and press to crisp, cook 7 to 8 minutes more.
Heat a large skillet with 2 tablespoons oil over medium to medium-high heat. Add cabbage, caraway, paprika, salt and pepper, cook stirring occasionally 2 to 5 minutes, until tender.
While cabbage and potatoes are working, preheat broiler. Heat a small skillet over medium heat with 2 tablespoons oil. Add chopped onions and a bay leaf, salt and pepper, cook 8 minutes until soft and sweet.
Pat meat dry and season with oil, salt and pepper. Broil the meat 10 to 15 minutes, ranging from medium-rare to medium-well doneness, turning once. Rest 5 minutes then thinly slice against the grain.
While meat cooks, add sugar and vinegar to the onions and stir 1 minute. Add beef stock and bring to a bubble. Reduce heat under gravy to low and stir in cream.
Stir the apple cider or juice together with mustard and pour over red cabbage. Stir to combine 1 minute then turn off heat.
Remove bay leaf from gravy. Serve cabbage and hash browns next to sliced steak topped with gravy.