Step 1

Make the cake: Preheat the oven to 350˚ F. Coat two 9-inch round cake pans with cooking spray and line the bottoms with parchment paper. Spray the parchment, then dust the bottom and sides of the pans with flour, tapping out the excess.

Step 2

Whisk together both flours, the baking powder, cinnamon, baking soda, salt, allspice and pepper in a medium bowl. In a large bowl, beat the vegetable oil, granulated sugar, maple sugar and the lemon zest with a mixer on medium-high speed until combined. Beat in the eggs, one at a time, then beat in both extracts. Reduce the speed to low and beat in the flour mixture in 3 additions, alternating with the buttermilk. Increase the speed to medium high and beat until well combined, about 1 minute. Fold in the carrots and raisins.

Step 3

Divide the batter evenly between the pans. Bake until the cakes are golden brown and the centers spring back when gently pressed, 35 to 40 minutes. Transfer to a rack and let cool 20 minutes in the pans, then remove the cakes to the rack, peel off the parchment and let cool completely.

Step 4

Make the frosting: Beat the cream cheese and butter in a large bowl with a mixer on medium-high speed until creamy. Reduce the mixer speed to low; add about half of the confectioners’ sugar and beat until it starts to incorporate. Add the remaining confectioners’ sugar, the extracts and salt. Beat to combine, scraping down the sides of the bowl as needed. Increase the mixer speed to medium high and beat until light and fluffy, about 4 minutes. Add the maple syrup and beat until incorporated, about 30 more seconds.

Step 5

Assemble the cake: Put 1 cake layer on a serving plate or cake stand and top with 1 1/2 cups frosting, spreading it almost to the edge. Top with the second layer. Spread a very thin layer of frosting over the top and sides of the cake (this is the crumb coat) and refrigerate until firm, 30 minutes to 1 hour. Frost the top and sides with the remaining frosting; scatter the candied walnuts on top. Refrigerate until ready to serve. Bring to room temperature about 20 minutes before serving.

Step 6

Melt butter in a skillet over medium heat. Add maple syrup, vanilla, ground cinnamon, salt and ground allspice. Bring to a simmer, then add the walnuts and cook, stirring, until bubbly, 1 to 2 minutes. Transfer to a parchment-lined baking sheet; bake at 350˚ F, stirring once, until the syrup is thick and the nuts are deeply browned, 8 to 10 minutes. Stir, then let cool and roughly chop.