Combine the cooled coffee, olive oil, vinegar, garlic, Dijon mustard, pepper, soy sauce, and brown sugar in a bowl. Pour the marinade mixture into a large food storage bag or non-reactive container and add the steak. Turn to coat the steak thoroughly with the marinade and then refrigerate for 2 to 4 hours, turning occasionally.
Discard the marinade and grill the steak over direct heat for 4 to 6 minutes on each side for medium rare.
Let the meat rest for about 5 minutes and then slice thinly on the diagonal across the grain.