"This delicious street food burger is very popular with my Ukrainian family. One of my baby cousins said it's a superman katletka. Ukrainian katleti are very similar but I must admit a little boring compared to the chimichurri. Don't be afraid to try this for your Eastern European family, they will absolutely love it. Before you know it, you won't be making katleti anyone, all chimichurri for our household! Enjoy and don't be afraid to let me know your outcome."
Mix ground beef, green bell pepper, finely chopped onion, Worcestershire sauce, soy sauce, yellow mustard, garlic, oregano, salt, and pepper together in a large bowl. Form mixture into 4 patties that will fit inside the rolls.
Heat vegetable oil in a large skillet over medium-high heat. Cook patties until browned on the bottom, about 6 minutes. Reduce heat to medium-low and flip; cook for 4 minutes. Top each patty with a slice of Cheddar cheese; cook until cheese starts to melt, about 2 minutes. An instant-read thermometer inserted into the center of each patty should read 150 degrees F (66 degrees C) for medium-well.
Mix ketchup and mayonnaise together in a small bowl. Spread evenly over both sides of each bun. Transfer a patty to each bun; top with sliced cabbage, tomatoes, and onion.