Preheat the oven to 350 degrees F.
Line the bottoms of three greased 9-inch round baking pans with parchment paper. Grease the parchment.
In a bowl, cream 1/2 cup of the butter and the brown sugar until light and fluffy, about 5-7 minutes.
Add the eggs to the butter mixture, one at a time, beating well after each addition.
Beat 1 teaspoon of the maple flavoring into the butter mixture.
In another bowl, whisk the flour, the baking powder, the baking soda, and 1/4 teaspoon of the salt together.
Add the butter mixture alternately with the buttermilk to the flour mixture, beating after each addition.
Transfer the batter evenly between the prepared pans.
Bake until a toothpick inserted in the center comes out clean, about 11-13 minutes.
Allow the cakes to cool in the pans for 10 minutes prior to moving them onto wire racks to cool completely. Discard the parchment paper.
While the cake is cooling, in a large skillet over medium heat, melt 1 tablespoon of the butter.
Add the walnuts to the melted butter and sauté the walnuts until toasted, about 5 minutes.
Stir 1 tablespoon of the maple syrup and 1/4 teaspoon of the salt into the walnut mixture and cook and stir for 1 minute.
Spread the candied walnuts onto foil to cool completely.
In a mixing bowl, mix the remaining butter until creamy.
Beat the remaining maple flavoring and the remaining salt into the butter mixture.
Gradually beat the confectioners' sugar and enough of the cream to reach the desired consistency into the frosting mixture.
Place 1 of the cooled cakes on a serving plate and spread with 1 cup of the frosting.
Sprinkle the frosting with 1/2 cup of the candied walnuts and drizzle with 1 tablespoon of the remaining maple syrup.
Repeat the layers once.
Top with the remaining cake and frost the top and the sides of the cake.
Sprinkle with the remaining walnuts and drizzle with the remaining syrup.
Slice and serve.