Mix the ground beef with panko breadcrumbs, egg, smoked paprika, garlic powder, onion powder, salt, and black pepper in a large bowl. Use your hands but don't overwork it—just fold everything together until combined. Overmixing makes burgers tough, and nobody wants that.
Divide the mixture into 4 equal portions and gently form into loose balls. Don't press them flat yet—that comes next on the skillet. Each portion should be roughly the size of a tennis ball.
Heat a cast-iron skillet over medium-high heat and melt 1 tablespoon butter. Once it's foaming, carefully place 2 beef balls on the skillet and smash them flat with a spatula for about 10 seconds. You want thin patties, roughly 1/4 inch thick.
Let the first batch cook for 2 to 3 minutes without moving them—this builds that crispy, golden crust you're after. Flip each patty and cook the other side for another 2 minutes. You'll see the edges get golden brown and hear them sizzle.
Top each patty with a slice of cheddar cheese during the last 30 seconds of cooking. The cheese melts perfectly over the warm beef. Remove these to a plate and repeat with the remaining butter and burger patties.
Toast the burger buns lightly in the skillet for about 30 seconds per side. I do this while the last burgers finish cooking, which saves time and adds texture. The buns get slightly crispy on the outside but stay soft inside.
Assemble your smash burgers by spreading BBQ sauce on the bottom bun. Layer the patty with melted cheese on top, then cap it with the toasted bun. Serve immediately while everything's still warm.