Preheat your oven to 350°F (175°C). Grease and lightly flour two 8-inch or 9-inch round cake pans and line the bottoms with parchment paper.
In a large bowl, stir together the flour, flax-seed meal, baking powder, pumpkin pie spice, baking soda, and salt; set aside.
In another large bowl, combine the finely shredded carrots, eggs (or egg product), granulated sugar, brown sugar, and oil.
Add the egg mixture all at once to the flour mixture and stir until just combined.
Divide the batter evenly between the prepared pans and bake for 20-30 minutes, or until a toothpick inserted into the center comes out clean.
Cool the cakes in the pans for 10 minutes, then invert them onto wire racks to cool completely.
To make the frosting, beat the softened cream cheese and vanilla with an electric mixer until smooth.
Gradually add powdered sugar if desired (or follow the light-whipped topping method), then fold in the whipped dessert topping to lighten the mixture.
Place one cake layer on a platter, top with half the frosting, add the second layer, and spread the remaining frosting on top.