Lay the flank steak strips out on a cutting board and drizzle with 1 tablespoon of oil. Evenly sprinkle with arrowroot, salt, and pepper. Using a spoon or your hands, mix well until evenly coated.
Heat up a large sauté pan over medium heat for 2 minutes. Add 2 tablespoons of oil, and let that heat through for another minute. Place the flank steak strips into the pan in a single layer, being sure not to overcrowd the pan. I like to do this in 2-3 batches. Cook for 5 minutes (2-3 minutes per side) until browned and crispy on the outside. Transfer to a plate.
Blanch the broccoli: bring a medium pot of water to a boil. Add in the broccoli florets and cook for 3 minutes. Drain thoroughly and dry as well as possible. Set aside.
Turn the stove back on to medium heat. Once the pan is hot, add onions and a big pinch of salt. Sauté for about 5 minutes, stirring occasionally until soft.
Add garlic and continue cooking for 1 minute, stirring often. Mix in broccoli florets and cook for about 4 minutes until tender. Add in ginger and continue stirring for 1 minute.
Place the cooked steak strips back into the pan (with their juices) and pour in the coconut aminos and fish sauce. Cook over medium to medium-low heat until the sauce has reduced down by about 1/2 to 2/3 and has slightly thickened, about 4-5 more minutes.
Remove from heat and serve alongside your favorite rice or cauliflower rice. Garnish with sesame seeds.