Grease a 6-inch round cake pan or springform that fits in your Instant Pot. Line the bottom with parchment if you want an easy release.
In a medium bowl, whisk together brown sugar, oil, egg, and vanilla until smooth.
Add carrots, stir to combine.
Sprinkle in dry ingredients: flour, baking powder, baking soda, spices, and salt. Stir gently just until mixed.
Pour batter into prepared pan and cover tightly with foil.
Place pan on a trivet inside the Instant Pot with 1 cup of water in the insert.
Pressure cook on High for 35 minutes. Natural release for 10 minutes, then quick release.
Let cool completely before glazing.