Preheat the oven to 350ºF. Line a 12 cup muffin tin with parchment paper cups and set aside.
In a mixing bowl, whisk the eggs with avocado oil until smooth. Stir in the nut butter, honey, shredded carrot, and vanilla. Add the remaining dry ingredients to the bowl, and stir until just combined.
Scoop the batter into the lined muffin tin, filling each up about 3/4 of the way full. Transfer to the oven and bake for 20 to 25 minutes, or until a toothpick inserted to the center of a muffin comes out clean.
Let cool in the muffin tin for 5 minutes before transferring to a cooling rack. Allow to fully cool before frosting.
To make your frosting, begin by softening the cream cheese and butter to room temperature so they mix easily. Add them to a large mixing bowl with vanilla and salt, and mix with a hand mixer on "low" until smooth & creamy. Add the powdered sugar a little at a time, and continue to mix until smooth.
Frost the cooled cupcakes and store at room temperature for up to 3-4 hours, otherwise transfer to the refrigerator to store. Remove from the fridge and give them a few minutes to come to room temperature before serving.