Place the steak in a large resealable plastic bag along with the oil, vinegar, orange zest, and 1 tablespoon of the parsley. Seal the bag and push the steak around to coat well, Refrigerate 1 hour.
Preheat and oil the grill. Remove the steak and marinade from the refrigerator and bring to room temperature. Remove the steak from the bag and season with salt and pepper to taste.
Place the mushroom caps into plastic bag. Seal the bag and push the mushrooms around to coat with marinade. Remove them from the bag and season with salt and pepper to taste. Discard plastic bag.
Grill the steak over direct medium-high heat about 10 minutes on each side for medium-rare or 12 minutes on each side for medium. Grill the mushrooms at the same time, top side down, on the edge of direct heat. Flip the mushrooms when you flip the steak and grill about 8 minutes longer, or until just beginning to char. Remove from the grill.
Remove the steak from the grill and let rest 5 minutes. Slice the steak and mushrooms into strips and arrange on a platter. Sprinkle with the remaining parsley and serve.