Step 1

Preheat the oven to 350 degrees F (175 degrees C). Generously grease and flour two 9-inch round cake pans.

Step 2

Whisk flour, cinnamon, baking soda, nutmeg, allspice, and salt together in a medium bowl.

Step 3

Whisk brown sugar, oil, applesauce, and white sugar together in a separate bowl. Whisk in eggs, one at a time, until combined. Switch to a large rubber spatula and scrape the sides and bottom of the bowl. Add dry ingredients in 3 parts, gently stirring until incorporated and batter is smooth. Stir in carrots and raisins. Divide batter evenly between the prepared cake pans.

Step 4

Bake in the preheated oven until the tops of the cakes spring back when lightly touched and a toothpick inserted in the centers comes out clean, 30 to 40 minutes. Remove from the oven and cool in the pans for 15 minutes before turning out onto cooling racks to cool completely, about 30 minutes. If you find that a cake layer is stuck to the bottom of the pan, leave the cake pan upside down and allow gravity to do its thing.

Step 5

While the cake is cooling, prepare the frosting. Melt butter in a skillet over medium-low heat. Cook, stirring occasionally until lightly browned, about 10 minutes.

Step 6

Transfer browned butter to a bowl. Add cream cheese and vanilla and beat with an electric mixer until smooth. Mix in cinnamon, cardamom, ginger, nutmeg, and allspice. Add powdered sugar, 1 cup at a time until desired taste and consistency.

Step 7

Frost cooled cake with cream cheese frosting and toasted pecans.