Preheat your oven to 350°F. Lightly grease your baking dish.
In a small bowl, whisk together flour, baking powder, cinnamon, allspice, and salt.
In a medium bowl, whisk together sugar, vegetable oil, and egg until well combined. Stir in flour mixture and use a rubber spatula to fold in grated carrots. Transfer batter to prepared baking dish.
Bake for 25 to 30 minutes, until a toothpick inserted into the center of the cake comes out clean. Place cake (in pan) on a cooling rack, and cool completely before frosting, about 45 minutes.
Frosting
Whisk together cream cheese, butter, and vanilla until smooth. Add sifted powdered sugar and salt and whisk until well-combined and fluffy. Spread frosting over the cake. Chilling before serving is optional but recommended.
Serve cake in the baking dish and enjoy!
Notes
Store cake covered in the refrigerator for up to 4 days. Approximate nutritional information is for 4 slices.