Prepare the beef by patting the flank steak dry with paper towels, then thinly slicing it against the grain into bite-sized strips. Place the sliced beef into a medium mixing bowl.
In a separate bowl, whisk together the low-sodium soy sauce, oyster sauce, brown sugar, rice vinegar, minced garlic, grated ginger, black pepper, and crushed red pepper flakes (if using) until the sugar is mostly dissolved and the mixture is well combined.
Pour about two-thirds of the sauce mixture over the sliced beef, reserving the remaining one-third in the bowl. Toss the beef until every strip is evenly coated, then sprinkle 1 tablespoon of cornstarch over the beef and toss again until the cornstarch disappears into the marinade. Let the beef marinate for at least 15 minutes at room temperature while you prepare the broccoli and air fryer.
While the beef marinates, place the broccoli florets in a large bowl. Drizzle with 1 tablespoon of olive oil and toss until the florets are lightly and evenly coated. Set the seasoned broccoli aside.
Preheat your air fryer to 390°F (200°C) for about 3 to 5 minutes so the basket is hot when the food goes in. While the air fryer preheats, lightly brush or rub the air fryer basket with 1 tablespoon of olive oil to help prevent sticking.
Arrange the marinated beef strips in a single layer in the preheated air fryer basket, allowing a little space between pieces so the hot air can circulate. Cook the beef at 390°F (200°C) for 6 to 8 minutes, shaking the basket or turning the pieces halfway through, until the beef is browned on the edges and just cooked through.
Carefully transfer the cooked beef to a large, clean bowl and cover it loosely to keep warm. Add the broccoli florets to the same air fryer basket, spreading them into an even layer. Air fry at 390°F (200°C) for 5 to 7 minutes, shaking the basket once or twice, until the broccoli is crisp-tender and lightly browned in spots.
While the broccoli cooks, return to the reserved sauce. Whisk the remaining 1/2 tablespoon of cornstarch into the sauce until no lumps remain. If the mixture seems very thick, whisk in 2 tablespoons of water to thin it slightly while still keeping it saucy.
Pour the reserved sauce mixture into a small skillet or saucepan and place it over medium heat on the stovetop. Bring it to a gentle simmer, whisking often, until the sauce thickens to a glossy, pourable consistency that lightly coats the back of a spoon, 2 to 3 minutes. Remove the pan from the heat.
When the broccoli is finished, transfer it to the bowl with the cooked beef. Pour the warm, thickened sauce over the beef and broccoli, then gently toss everything together until all the pieces are evenly coated and glistening with sauce.
Taste a piece of beef and broccoli and adjust the seasoning if needed, adding a small splash of soy sauce for more saltiness or a pinch of crushed red pepper flakes for extra heat. Serve the beef and broccoli air fryer dish hot, enjoying it right away while the beef is tender and the broccoli is still crisp-tender.