Step 1

Combine cheese, flour, and milk in a small bowl and toss with a spoon to combine. Divide mixture evenly between two small ramekins and set aside. Set a steamer insert into a large saucepot with 1 inch of water. Bring water to a simmer over medium-high heat and cover pot.

Step 2

Heat vegetable oil in a 10-inch cast iron or stainless steel skillet over high heat until smoking. Add beef balls to skillet and smash firmly with a stiff spatula into 4- to 4 1/2-inch patties. Season generously with salt and pepper.

Step 3

While patties cook on first side, transfer cheese cups to steamer and close lid. After the first side is well browned (about 1 1/2 minutes), carefully scrape patties up from bottom us skillet using a stiff spatula and flip. Season top side with salt and pepper. Continue to cook until second side is browned, about 1 minute longer.

Step 4

Transfer patties to toasted bun bottoms. Carefully pick up a ramekin full of cheese with a pot holder and stir with a spoon until homogenous and completely smooth. Scrape cheese out of ramekin over burger. Repeat with second burger. Serve immediately with condiments and toppings as desired.