Preheat the oven to 400 F degrees. Grease 2 (8 x 2-inch) round cake pans, line the bottoms with parchment paper, and grease the flour the pans.
In medium bowl, sift together the 2 cups of flour, cinnamon, baking soda, and salt. Set aside.
In the bowl of an electric mixer fitted with the paddle attachment, beat the sugar, oil, and eggs on medium-high speed for 2 minutes, until light yellow and thickened. Stir in the vanilla.
With the mixer on low, slowly add the dry ingredients to the wet ones.
In a medium bowl, toss the carrots, raisins, walnuts, and the 1 tablespoon of flour. Stir into the batter with a rubber spatula. Divide the batter between the prepared pans and smooth the tops. Bake for 10 minutes, lower the heat to 350 degrees, and bake for 30 to 35 more minutes, until a toothpick comes out clean. Cool in the pans for 15 minutes, turn out onto baking rack, and cool completely.
Place one cake on a flat serving plate, rounded side down, spread half the frosting on the top (not the sides). Place the second cake on top of the first cake, rounded side up. Frost just the top of the second cake.