Set Instant Pot to sauté.
Add the butter and allow it to sizzle.
Add the eggs and cook for 1-2 minutes or until the eggs begin to firm.
Flip the eggs and cook for about 30 seconds.
Remove cooked egg, cut into thin strips, and set aside.
Give the Instant Pot a quick wipe.
Set the Instant Pot to sauté. Add olive oil and garlic and cook for 1-2 minutes.
Add the beef and brown on each side.
In a small bowl, add vinegar, hoisin and soy sauces, ginger, and brown sugar. Whisk together and reserve 1/4 cup.
Pour remainder of sauce into Instant Pot, covering the beef.
Set the Instant Pot to high pressure for 35 minutes. Allow it to release naturally for 15 minutes.
Using two forks, shred the beef.
Add the mushrooms and 2 cups of the coleslaw mix.
Set the Instant Pot to high pressure for 3 minutes. Allow pressure to release naturally for 5 minutes. Turn off Instant Pot.
Add 2 Tablespoons of Moo Shu Beef to a lettuce cup. Add a few slices of egg and a bit of the coleslaw mix. Drizzle with sauce.
Freeze Ahead Instructions:
Skip cooking the eggs but complete the other Instant Pot steps. Place the cooked beef and vegetable mixture into a resealable freezer bag, seal, and freeze. On the day of cooking, take it out to thaw. Reheat in the microwave. Fry an egg up on the stove and assemble the lettuce wraps by adding the beef and vegetables, fried egg, and sauce to lettuce leaves.