Mix mayonnaise, ketchup, Worcestershire sauce, and a pinch of smoked paprika in a small bowl until smooth, then refrigerate.
Divide ground beef into 4 equal portions, gently shape into patties, press a shallow indent in the center of each with your thumb, and season both sides with smoked paprika and salt.
Preheat a cast iron skillet or grill over medium-high heat, cook patties for 4 minutes per side without pressing, flipping only once, until internal temperature reaches 160°F / 71°C.
Add one cheese slice to each patty in the last 60 seconds of cooking and cover the pan to melt.
Toast buns cut-side down in the same pan for 1 to 2 minutes until golden.
Spread BBQ sauce on bottom bun, layer lettuce, patty with cheese, tomato slice, and top bun.