Put the eggs, oil, sugar, orange juice, and vanilla in a bowl. Mix. Add the flour, baking powder, and salt. Stir. Add the carrot, walnuts, and orange zest. Stir.
Grease a 7.5 in (19 cm) cake pan. Pour the batter into the pan and cover with aluminum foil to seal.
You can use the Instant Pot removable round bake pan for this.
In the Instant Pot® bowl, add 1 ½ cups of water, the rack and the mold on top.
Close and lock the Instant Pot® lid. Make sure the steam release handle is turned to Sealing. Press Pressure Cook, pressure level High, and set time to 1 Hour 45 Minutes.
Once that time is up, press Cancel and turn the steam release handle to Venting. Once all the pressure has been released, take off the lid, and remove pan.
Let cool for at least 15 minutes before unmolding.
For the icing, put all the ingredients in a bowl. Beat until the mixture is homogeneous. Garnish the carrot cake with the icing.