1. Place a large non-stick skillet over medium heat. Add 1/2 tablespoon of the vegetable oil to the pan followed by the sliced onions, salt, and pepper.
2. Cook until the onions become tender, then reduce to a low heat and continue cooking until the onions are caramelized, about 7 minutes more.
3. While the onions are cooking, make the patties. Place the ground beef, Worcestershire sauce, and steak seasoning in a large bowl. Knead with your hands to combine, then form into 4 long patties, a little bit wider than the slices of rye bread.
4. Place a large non-stick skillet over medium-high heat. Add the remaining 1/2 tablespoon of vegetable oil, followed by the patties. You may do this in 2 batches if your skillet is not large enough to hold all 4 patties.
5. Cook the patties until they are browned, about 5 minutes per side. Transfer to a plate and top each patty with an even amount of crumbled blue cheese.
6. Place a large grill pan or non-stick skillet over medium-high heat. Place 4 pieces of rye bread on the pan, then top with a blue cheese topped patty and an even amount of the caramelized onions.
7. Cook until the bread is toasted, about 3 minutes, then flip and toast on the other side.