Set the Instant Pot to saute and add the olive oil. Wait one minute for the oil to heat up and then add the chicken, green onion, and carrot.
Saute for 1 minute, stirring often.
Add the artichokes, dill, water, salt, and pepper. Stir well.
Put the top on the Instant Pot and lock it. Set the vent to "sealing" to lock in the pressure.
Set the manual time to 7 minutes. Walk away and let the Instant Pot work its magic.
Once the timer reaches 0, wearing an oven mitt, carefully set the vent to "venting" which will release the pressure.
Whisk together the lemon juice and eggs in a bowl. Take a ladle of the hot broth from the Instant Pot and slowly ladle it into the eggs and lemon while continuously whisking. You need to bring up the temperature of the eggs before adding it back to the pot.
Slowly pour a second ladle of hot broth into the eggs while continuously whisking.
Pour this mixture into the chicken and artichokes and immediately stir well. Now the egg-lemon sauce has been incorporated into the chicken and artichokes and you're ready to eat. Serve with black pepper and extra lemon slices to garnish.