Add ground beef, egg, breadcrumbs, salt, pepper, and Worcestershire sauce into a large bowl. Mix gently until just combined and the texture looks even. Do not overmix or the patties will become tough.
Divide the mixture into 4 equal portions and shape into round patties about 4–5 inches wide. The surface should look smooth but slightly firm.
Press a light thumb indent in the center of each patty if they are thick. This helps them cook evenly and stay flat while cooking.
Heat olive oil in a heavy pan over medium-high heat until slightly shimmering. Place patties in the pan and listen for a steady sizzle.
Cook for 5–6 minutes on the first side until a brown crust forms. Flip carefully when the edges look golden and slightly crisp.
Cook the second side for another 5–6 minutes until fully browned and juicy. Avoid pressing down so the juices stay inside.
If using cheese, place a slice on top during the last minute and let it melt. The surface should look glossy and soft.
Remove from heat and rest for 2–3 minutes before serving. This helps the juices settle inside the patties.