Combine the ground beef, breadcrumbs, ketchup, dry mustard, Worcestershire sauce, bouillon and some salt and pepper. Knead until all combined. Form into 4 to 6 oval patties, and then make lines across the patties to give them a “steak” appearance.
Fry the patties in a skillet with the butter and oil over medium-high heat on both sides until no longer pink in the middle. Remove from the skillet and pour off any excess grease.
For the gravy
Reduce the heat to medium and add in the sliced onions. Stir and cook until golden brown and somewhat soft, for several minutes. Add the beef stock, ketchup, seasoning sauce, if using, and the Worcestershire. Then combine the cornstarch with a little beef broth and add to the sauce if using. Stir and cook to reduce.
Add a sprinkle of salt and pepper and more broth if needed for thinning. Then return the patties to the gravy. Spoon the gravy over the top and let them simmer and heat back up for a couple of minutes.
For the carrots
In a large skillet, cook butter over medium heat, stirring frequently, until it begins to brown. Add carrots, salt, and pepper; cook 8 to 10 minutes, stirring occasionally, just until carrots are tender.
Pour water into skillet. Cover; cook 10 minutes. Stir in brown sugar and vinegar; cook uncovered 8 to 10 minutes or until carrots are glazed and most of liquid has evaporated. Remove from heat; stir in vanilla.