Preheat oven to 350°F (175°C). Grease and flour two 9-inch round cake pans (or one 9×13-inch pan).
In a large bowl, whisk together the sugar and vegetable oil until well combined. Add eggs one at a time, beating well after each addition.
In a separate bowl, whisk together the flour, baking soda, baking powder, cinnamon, allspice, and salt.
Gradually add the dry ingredients to the wet mixture, stirring just until combined. Add in grated carrots and pecans.
Pour batter evenly into prepared pan(s). Bake for 30–35 minutes for round pans (or 40–45 minutes for a 9×13), or until a toothpick inserted in the center comes out clean.
Let cakes cool in pans for 10 minutes, then remove to wire racks and cool completely before frosting.
In a large bowl, beat the softened butter and cream cheese until smooth and creamy.
Gradually beat in the confectioners' sugar. Add vanilla and sweet cream, then beat until light and spreadable.
Spread icing between cake layers (if using rounds) and over the top and sides. Slice and serve.
