Cut the beef slices to an even thickness (about 2 cm thick), then brush both sides with olive oil.
Season the beef with salt, black pepper, garlic powder, and Worcestershire sauce. Let it rest at room temperature for 10 minutes.
Heat a skillet or grill to medium-high heat. Cook the beef for about 3-4 minutes per side, until nicely browned but still juicy inside.
In the last minute of cooking, place a slice of cheddar cheese on each beef slice and cover to let it melt.
Halve the hamburger buns and lightly toast the cut sides in a dry skillet.
Spread a little mayonnaise and Dijon mustard on the bottom bun. Top with lettuce leaves, then the cheese-covered beef slice. Add thinly sliced tomato and finally the top bun.
Serve the burger immediately, with french fries or other side dishes.
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