Preheat the oven to 350 degrees. Grease two 9x5 loaf pans. With an electric mixer on low, beat together the eggs, oil, sugar, brown sugar, and buttermilk. When combined, stir in the flour, baking soda, baking powder, cinnamon, allspice, salt and carrots. Divide the batter evenly between the two pans. Bake for 40 minutes, until a toothpick comes out clean. Remove from oven and let cool for 15 minutes before removing from pans. Combine the cream cheese, powdered sugar, and vanilla until well combined. Spread over the two cakes and serve.