In a medium saucepan over medium-high heat, saute the shallots in 2 tablespoons of the olive oil until lightly caramelized, about 5 to 7 minutes. Raise the heat to high and add the red wine and reduce by half. Add the broth and reduce by half. Check for seasoning, and season with salt and pepper, to taste. Keep warm on low heat.
Brush the flank steak on both sides with 2 tablespoons of the olive oil and season with the salt and pepper. Place on the center of grill and sear 5 to 8 minutes per side for rare to medium rare, testing by pressing the meat with a finger: The spongier the meat feels, the rarer it is cooked. Remove from the grill and allow to rest, very loosely tented with aluminum foil, 5 to 10 minutes, to allow the juices to reabsorb into the meat. Slice the flank steak on the diagonal and place on a large platter. Finish the sauce by swirling in the chunks of cold butter, then top the steak with some of the sauce and serve the rest on the side.