Place ginger root, garlic, soy sauce, 1 cup water, brown sugar, and hoisin sauce in a medium bowl. Stir well to combine.
Set your Instant Pot to the saute setting. Add olive oil. When olive oil is heated, add beef and saute for 2 to 3 minutes, stirring frequently.
Pour mixture over beef and stir to combine. Add carrots and stir again.
Turn Instant Pot off. Place the lid on and lock. Steam release knob should be set on “sealing”.
Cook on manual setting (high pressure) for 10 minutes. Allow the pressure to naturally release for 10 minutes, then quick release remaining pressure.
Carefully remove lid and stir. Turn off Instant Pot.
Prepare the cornstarch slurry by whisking together cornstarch and ⅓ cup cold water in a small bowl or large measuring cup until smooth. Add to sauce and stir to combine. Turn on the saute setting and continue to stir until slightly thickened (about 2 minutes). Turn off your Instant Pot. Sauce will thicken as it sits (about 5 minutes).
Serve over cooked white rice (if desired) and top with sliced green onions and sesame seeds.