Heat oven to 350°F. Grease two 9-inch round cake pans with shortening; lightly flour. In large bowl, mix flour, granulated sugar, baking powder, baking soda, salt and cinnamon. Add applesauce, oil and eggs; beat with electric mixer on low speed until moistened. Beat on high speed 2 minutes. Stir in pecans. Pour batter into pans.
Bake 30 to 40 minutes or until toothpick inserted in center comes out clean. Cool 10 minutes; remove from pans. Cool completely.
In small heavy saucepan, brown butter over medium heat, stirring constantly, until light golden brown. Remove from heat; cool completely. In large bowl, beat browned butter, powdered sugar and 4 tablespoons of the apple juice with electric mixer on low speed until moistened. Continue beating until well blended, adding additional apple juice until desired spreading consistency. Fill and frost cake.