Heat oven to 350 degrees. Grease and flour two 9" cake pans.
Spoon flour into measuring cup; level off. In large bowl, combine flour, sugar, baking soda, baking powder, salt and cinnamon.
Add applesauce, oil and eggs; blend on low till moistened. Then beat 2 minutes on high.
Stir in pecans. Pour batter into prepared pans. Bake till toothpick or cake tester inserted comes out clean. Cool 10 minutes; then remove from pans.
FROSTING: Cool cake completely. In small heavy saucepan over medium heat, brown butter till light golden brown, stirring constantly.
Remove from heat; cool completely. In large bowl, combine browned butter, powdered sugar and 4 TBSP. of apple juice; blend on low till moistened.
Continue beating till well blended, adding additional apple juice until of spreading consistency. Fill and frost cake. Garnish with pecans, if desired.
NOTE: Walnuts work just as well and give great flavor.