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1
In a medium bowl, gently mix together beef with vinegar, making sure to mix only as long as it takes to just combine them (overmixing the meat will cause it to form a tighter, more meatloaf-like texture, so make sure not to do it any more than necessary). Form 2 patties slightly wider than the width of the buns, press a dimple in the center of each with your thumb, and season all over with salt. Refrigerate for at least 30 minutes and up to 1 hour.
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2
Meanwhile, in a small bowl, stir together olives and mayonnaise. Refrigerate until ready to use.
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3
When all the charcoal is lit and covered with gray ash, pour out and spread the coals evenly over half of coal grate. Alternatively, set half the burners of a gas grill to high heat. Set cooking grate in place, cover grill and allow to preheat for 5 minutes.
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4
and
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5
the grilling grate.
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6
Place patties directly over hot coals and cook, turning occasionally, until well charred and center of burgers register 110u00b0F (43u00b0C) on an instant-read thermometer, about 7 minutes. Place 2 slices of cheese on top of each patty and continue to cook until cheese is melted and burgers register 125u00b0F (51u00b0C) for medium rare or 135u00b0F (57u00b0C) for medium, 1 to 2 minutes longer. Transfer burgers to a large plate and let rest 5 minutes. (Move burgers to cooler side of grill at any time if they threaten to burn but haven't reached their final internal temperature yet.)
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7
Toast buns over coals. Spread olive mayonnaise on top and bottom halves of each bun. Set patties on bottom buns, close burgers, and serve right away.
