Combine the shallots, thyme, brown sugar, soy sauce, Worcestershire sauce, vinegar, and oil in a freezer-type zip-top plastic bag. Add the steaks. Squeeze out as much air as possible and seal the bag. Place the bag in a medium bowl in the refrigerator to marinate overnight, turning bag several times for even coating.

Heat a grill.

Drain the steaks, reserving the marinade. There will not be much. Pour the marinade into a small saucepan. Rinse the bag with 1/4 cup water and add to marinade. Simmer 4 to 5 minutes and stir in the butter.

Grill steaks to medium-rare, about 2 minutes each side.

Let stand 4 to 5 minutes before slicing. Thinly slice at an angle across the grain, which runs up and down the short side of the steak. Bring the marinade-butter mixture back to a boil, pour over the meat, and serve immediately.