Combine the olive oil, red wine vinegar, Worcestershire sauce, garlic, salt and freshly ground black pepper in a non-reactive container or zipper sealable plastic bag. Add the skirt steak to the bag and massage the marinade into both sides of the meat. Refrigerate for 6 hours to overnight, turning the bag over halfway through the marinating process.
To make the dressing, combine the balsamic vinegar, honey, mayonnaise, Dijon mustard, salt, pepper, and parsley in a bowl or food processor. While mixing or processing, slowly add the olive oil and whisk (or process) until the dressing is thickened and emulsified. Chill until ready to use.