DO-AHEAD TIP: Marinate flank steak overnight or for at least 8 hours (see recipe).
In a large zipper-topped plastic bag, combine first 8 ingredients (wine through garlic); pour off 1/4 cup of this marinade, cover it tightly and refrigerate for later use.
Place flank steak in the bag with remaining marinade; seal bag and turn to coat. Refrigerate overnight or for at least 8 hours, turning occasionally.
Preheat indoor or outdoor grill to MEDIUM.
Remove steak from marinade, and grill for 8 to 12 minutes, brushing with reserved marinade until it reaches the desired level of doneness.
Meanwhile, transfer marinade from plastic bag to small saucepan; bring to a boil over medium heat; cook for 5 minutes then remove from heat.
Remove steak from grill to a cutting board and let it rest for 10 minutes. Meanwhile, steam broccoli and prepare noodles.
Thinly slice steak across the grain (diagonally); serve over noodles with steamed broccoli, and drizzle the sauce over all.