Preheat the oven to 350 degrees. Prepare an 8x8 baking dish with nonstick cooking spray.
Whisk together the flour, baking soda, cinnamon, salt and sugar in a large mixing bowl.
Combine the beaten eggs, oil, and vanilla and stir into the dry mixture. Stir until the ingredients are moistened. Add the shredded carrots and stir until all ingredients are truly mixed. The batter will be thick.
Transfer the batter to the prepared baking dish.
Bake for 35 to 45 minutes or until a toothpick comes out clean. Let the cake cool in the baking dish until completely cooled.
Meanwhile, prepare the icing by beating the butter and cream cheese at medium speed until light and fluffy, about 6 minutes, scraping down halfway. Add the powdered sugar and vanilla, beating at low speed until mixed and then medium speed until fluffy.
When the cake is cooled, scrambled the cake with two forks. Stir the icing into the cake until completely mixed.
Prepare a large rimmed baking sheet with waxed or parchment paper. Portion the cake using a 1 inch scoop and roll into balls. Place the balls on the prepared baking sheet and freeze for at least 20 minutes.
Place the white chocolate morsels into a microwave safe bowl with the shortening or coconut oil. Microwave in 30 second increments, stirring well between each heating, until the chocolate is completely melted.
Dip the cake balls into the melted chocolate allowing the excess to run back into the bowl. Place the covered cake balls on wax or parchment paper and sprinkle immediately with chopped pecans. Allow the chocolate to set completely before serving.
Store in an airtight container between layers of waxed or parchment paper in the refrigerator or freezer. If frozen, allow to thaw before serving.