In a medium bowl, toss the thinly sliced flank steak with 1 tbsp cornstarch, 1 tbsp soy sauce, and 1 tsp sesame oil until evenly coated. Set aside to marinate for at least 10 minutes.

In a small bowl, whisk together the beef broth, 1/4 cup soy sauce, brown sugar, grated ginger, and minced garlic. In a separate small bowl, mix 1 tbsp of cornstarch with 2 tbsp of cold water to make a slurry. Set aside.

Heat vegetable oil in a large skillet or wok over medium-high heat. Add the beef in a single layer and cook for 1-2 minutes per side, until browned. Work in batches if necessary. Remove beef from the skillet and set aside.

Add broccoli florets and 2-3 tablespoons of water to the hot skillet. Cover and steam for 3-4 minutes until crisp-tender.

Return the beef to the skillet with the broccoli. Pour the sauce mixture over the top and bring to a simmer. Add the cornstarch slurry and stir constantly for 1-2 minutes until the sauce thickens. Remove from heat and stir in the remaining 1 tsp of toasted sesame oil. Serve immediately.