Stir together the marinade ingredients then add the flank steak. Let rest either at room temperature for 10 minutes, or refrigerate overnight.
Preheat the broiler and place the rack about 4 inches from the top of the oven. Prepare a baking sheet by lining with foil or by lightly greasing. If you have a wire rack to set on the baking sheet, or a broiler pan, even better.
Broil until medium-rare, about 8 to 10 minutes. Remove from oven and let rest 5 minutes, then slice against the grain.
In a large bowl, toss together the spinach, carrots, red onion, and sprouts. Set aside and whisk together the dressing ingredients in a separate bowl or measuring cup.
Add about all but 2 tbs of the dressing to the salad, then toss. Top with steak slices, then drizzle on the remaining dressing.
Sprinkle on the sesame seeds, then serve warm as is, or prepare ahead of time for an excellent lunch.