Make diagonal cuts through the skirt steak on both sides. Cut diagonally about every 1/4 to 1/2 inch, then cut diagonally in the opposite, perpendicular direction. Repeat on the other side of the steak to complete the crisscross cuts that will tenderize the meat. When the meat is prepared, some sections will be very long. I cut the longer sections to keep them under 18 inches long.
Whisk together the olive oil, red wine, parsley, basil, balsamic vinegar, soy sauce, garlic, and bay leaves in a large glass or ceramic bowl. Add the skirt steaks and toss to evenly coat. Cover the bowl with plastic wrap, and marinate in the refrigerator for 8 hours to overnight.
Preheat an outdoor grill for medium heat, and lightly oil the grate. Remove the skirt steaks from the marinade, and shake off excess. Discard the remaining marinade.
Cook the skirt steak on the preheated grill to your desired degree of doneness, about 10 minutes per side for medium-well. Once nearly finished, brush the steaks with the barbeque sauce and cook for 2 minutes. Flip the steaks over, brush with barbeque sauce, and cook 2 minutes longer.
