Combine ground beef, breadcrumbs, egg, minced onion, garlic, salt, pepper, paprika, cayenne, and Worcestershire sauce in a large bowl. Mix gently with your hands for exactly 30 seconds—overworking develops gluten strands that create dense, rubbery patties. The mixture should just come together with visible specs of garlic and onion remaining.
Divide the mixture into 4 equal portions, each approximately 8 ounces. Roll each portion gently into a ball without compacting, then flatten into a 3/4-inch-thick disc. Create a slight depression in the center using your thumb—this prevents the patty from puffing into a dome during cooking. Refrigerate patties for minimum 30 minutes; this allows flavors to meld and helps stunning homemade beef burger patties maintain their shape on the heat.
Heat olive oil in a cast-iron skillet or griddle over medium-high heat until just smoking. The surface temperature should reach 375°F for optimal crust development. Place each beautiful beef burger patty carefully onto the hot surface and resist the urge to move it—let it sear undisturbed for exactly 4 minutes.
Flip the patties once using a thin spatula, pressing gently downward to ensure full contact with the cooking surface. Top each with a slice of cheddar cheese immediately after flipping. Cook for 3-4 minutes until the internal temperature reaches 160°F using an instant-read thermometer inserted horizontally into the thickest part. The cheese should be fully melted before removing from heat.
Transfer cooked patties to a warm plate and rest for 2 minutes before assembling. Toast your burger buns lightly in the residual skillet heat—this adds textural contrast and prevents sogginess. Spread mayonnaise on the bottom bun, layer lettuce, add your perfectly cooked patty with melted cheese, and top with tomato slices and the upper bun.