Add the soy sauce, water, brown sugar, rice vinegar, sesame oil, red pepper flakes to the instant pot; mix to combine. Add the sliced beef, carrots, garlic, and ginger; mix until everything is well coated in the sauce.
Secure the lid to the instant pot and turn the venting knob to sealing position. Select "pressure cook", adjust the time to 10 minutes.
When the time is over, let the pressure release on its own for 5 minutes. Then, carefully turn the vent to "Venting," to release any extra pressure that might still be in there. Press “cancel”. Then remove the lid.
In a small bowl mix cornstarch with ¼ cup water. Add the mixture to the beef; mix to combine.
Turn the Instant Pot on and select "sauté" mode, adjust heat to normal. Let the beef simmer for 3-4 minutes, or until the sauce thickens.
Garnish green onion slices and sesame seeds, if desired. Serve immediately over rice or steamed vegetables.