In a large mixing bowl, combine the ground beef, chopped onion, Worcestershire sauce, garlic powder, smoked paprika, salt, and black pepper. Use your hands to mix gently until just combined, being careful not to overwork the meat.
Divide the mixture into 4 equal portions and shape each into a patty about 3/4 inch thick, slightly larger than the buns to account for shrinkage during cooking.
Heat a large skillet or grill pan over medium-high heat and add the vegetable oil. Once the oil is shimmering, carefully place the patties in the pan, leaving space between them.
Cook the patties for 4-5 minutes on the first side, or until a deep brown crust forms. Flip the patties and cook for another 3-4 minutes, then place a slice of cheddar cheese on each patty during the last minute of cooking to melt.
While the patties cook, lightly toast the hamburger buns on the skillet or in a toaster until golden brown.
Assemble the burgers by placing a patty on the bottom half of each bun. Add desired toppings such as lettuce, tomato, and pickles, then top with the other half of the bun. Serve immediately.