Divide the ground beef into two loosely packed balls, about 4 ounces each. Place the balls on a clean surface and gently form them into rough, round shapes, avoiding overworking the meat.
Heat the cast-iron skillet over medium-high heat until hot and slightly smoking. Place the beef balls onto the skillet, spacing them apart.
Using a heavy spatula or burger press, immediately press each beef ball down firmly until they flatten to about ¼ inch thickness. Cook for about 2 minutes without moving, until edges begin to brown.
Carefully flip the patties and cook for another 1-2 minutes, until they develop a deep brown crust and are cooked through (internal temperature of 160°F). Optionally, add cheese slices during the last 30 seconds to melt.
While the burgers are cooking, toast the burger buns in the same skillet until golden brown on the cut sides, about 1 minute.
Assemble the burgers by placing each patty on a toasted bun. Add desired toppings and condiments. Serve immediately, showcasing the crispy edges and juicy interior.