Add beef broth, soy sauce, brown sugar, sesame oil, garlic, and ginger to your Instant Pot. Stir to combine.
Add the sliced beef and stir to coat with the sauce.
Close the lid, set the valve to sealing, and cook on high pressure for 12 minutes.
When cooking is complete, do a quick release of the pressure.
Add the broccoli florets on top of the beef (don't stir yet). Close the lid and let sit for 3 minutes to steam the broccoli.
Remove the broccoli and beef with a slotted spoon and set aside.
Mix cornstarch and water in a small bowl. Turn the Instant Pot to sauté mode and add the cornstarch slurry, stirring constantly until sauce thickens (about 2 minutes).
Return beef and broccoli to the pot, toss with sauce, and serve over rice or noodles.