Preheat oven to 350°. Line bottoms of 3 greased 9-in. round baking pans with parchment; grease parchment.
Cream butter and brown sugar until light and fluffy. Add 1 egg at a time, beating well after each addition. Beat in maple flavoring. In another bowl, whisk together flour, baking powder, baking soda and salt; add to creamed mixture alternately with buttermilk, beating after each addition.
Transfer to prepared pans. Bake until a toothpick inserted in center comes out clean, 11-13 minutes. Cool in pans 10 minutes before removing to wire racks; remove paper. Cool completely.
For candied walnuts, in a large skillet, melt butter over medium heat; saute walnuts until toasted, about 5 minutes. Stir in maple syrup and salt; cook and stir 1 minute. Spread onto foil; cool completely.
For frosting, beat butter until creamy. Beat in maple flavoring and salt. Gradually beat in confectioners' sugar and enough cream to reach desired consistency.
Place 1 cake layer on a serving plate; spread with 1 cup frosting. Sprinkle with 1/2 cup candied walnuts and drizzle with 1 tablespoon maple syrup. Repeat layers.
Top with remaining layer. Frost top and sides of cake. Top with remaining walnuts and syrup.