Place one rack on the lower third rung in the oven, and the other in the upper third. Have two baking sheets ready.
Form the beef into 4 equal sized balls. Place on a plate till ready to cook. Don't pack the meat tightly, a bit looser will help them spread out when you smash them.
Cook for 1 1/2-2 minutes till the edges are seared and the burger releases. Flip and cook for 30 seconds. Add the cheese over each burger and cover with a large stock pot lid or other lid. After 1 minute the burger should be done and the cheese melted. Transfer the burgers to the other baking sheet. Repeat with the remaining butter and burgers. Place the baking sheet onto the lowest rack in the oven.
See blog post for more details including how to do this on an outdoor grill.