To prepare the cake, preheat the oven to 350°F. Cut two 9”-round circles out of wax paper to fit inside two 9”-round cake pans. Lightly coat the two 9”-round cake pans with nonstick cooking spray. Gently press one wax paper circle into the bottom of each cake pan, and lightly coat the wax paper with nonstick cooking spray.
In a large bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt. In a separate bowl, whisk together the coconut oil, egg whites, and vanilla. Stir in the Greek yogurt, mixing until no large lumps remain. Mix in the maple syrup and stevia. Alternate between adding the flour mixture and the milk, beginning and ending with the flour mixture, and stirring just until incorporated. (For best results, add the flour mixture in 4 equal parts.) Gently fold in the carrots.
Divide the batter between the prepared pans. Bake at 350°F for 24-28 minutes, or until the center feels firm to the touch and a toothpick inserted into the center comes out clean. Cool in the pans for 10 minutes before inverting, peeling off the wax paper, and transferring to wire racks to cool completely.
To prepare the frosting, add the Greek yogurt, cream cheese, and stevia to a medium bowl, and beat with an electric mixer until smooth. To assemble the cake, spread a generous dollop of frosting on top of one of the cake layers. Place the second layer on top. Frost the tops and sides.