Preheat oven to 325°.
To prepare cake, lightly spoon flour into a dry measuring cup; level with a knife. Combine flour, 1/2 cup granulated sugar, brown sugar, and nutmeg, stirring with a whisk.
Place egg whites in a large bowl; beat with a mixer at high speed until foamy. Add cream of tartar and salt; beat until soft peaks form. Add 1/2 cup granulated sugar, 2 tablespoons at a time, beating until stiff peaks form. Beat in extracts.
Sift 1/4 cup flour mixture over egg white mixture; fold in. Repeat procedure with flour mixture, 1/4 cup at a time.
Spoon batter into an ungreased 10-inch tube pan, spreading evenly. Break air pockets by cutting through batter with a knife. Bake at 325° for 50 minutes or until cake springs back when lightly touched. Invert pan; cool completely. Loosen cake from sides of pan using a narrow metal spatula. Invert cake onto plate.
To prepare topping, combine powdered sugar and maple syrup in a small bowl, stirring with a whisk until smooth. Drizzle sugar mixture over top of cake; sprinkle with walnuts.