Slice the flank steak against the grain into thin slices. Put the slices into a mixing bowl with the brown sugar, rice vinegar, soy sauce, ginger, lemon juice, red pepper flakes, and crushed garlic. Marinate at least 1 hour.
Spread the broccoli florets and sliced garlic cloves out onto a baking sheet that has been sprayed with nonstick spray. Season with salt and pepper and drizzle with olive oil. Roast the broccoli in a 400 degree oven for about 20 minutes.
When the broccoli is done, heat a large skillet to high heat. Put the flank steak in with all of its marinade juices. Cook until the meat reaches desired level of doneness. Flank steak cooks quickly so this should only take a few minutes.
Combine steak with roasted broccoli and serve over steamed rice. Garnish with lemon zest.