Make the frosting: Whisk the egg whites and maple sugar in a heatproof bowl set over a saucepan of simmering water (do not let the bowl touch the water) until the mixture is warm and the sugar dissolves, about 5 minutes. Remove the bowl from the pan and beat with a mixer on high speed until stiff, shiny peaks form, about 5 minutes. Beat in the butter a few pieces at a time, then continue beating until smooth. (Don't worry if the mixture looks separated at first; keep beating and it will come together.) Beat in the maple extract.

Assemble the cake: Poke holes all over the tops of the 2 cake layers using a toothpick. Spoon the reserved walnut syrup over the cakes, letting it soak into the holes.

Coarsely chop the walnuts. Transfer 1 cup frosting to a medium bowl; fold in the chopped nuts. Put 1 cake layer on a platter and spread the walnut frosting on top. Top with the second cake layer. Cover the whole cake with the remaining maple frosting. Decorate with more walnuts.

Photograph by Levi Brown