To prepare cake, beat the first 3 ingredients with a mixer at low speed until well-blended (about 5 minutes). Add applesauce; beat well. Lightly spoon flour into dry measuring cups, and level with a knife. Combine flour and next 5 ingredients (flour through salt), stirring well with a whisk. Add flour mixture to applesauce mixture; beat just until moist. Stir in raisins, pecans, and 1 teaspoon vanilla.
Spoon the batter into 2 (9-inch) round cake pans coated with cooking spray. Bake at 350° for 35 minutes or until a wooden pick inserted in center comes out clean. Cool in pans 10 minutes on a wire rack; remove from pans. Cool completely on rack.
To prepare icing, combine 1 cup brown sugar, milk, butter, and 1/4 teaspoon salt in a medium saucepan; bring to a boil over medium-high heat, stirring constantly. Reduce heat, and simmer until slightly thick (about 5 minutes), stirring occasionally. Remove from heat. Add the powdered sugar and 1 teaspoon vanilla; beat with a mixer at medium speed until smooth and slightly warm. Cool 5 minutes (icing will thicken as it cools).
Place 1 cake layer on a plate; working quickly, spread with 1/3 cup icing, and top with remaining layer. Spread remaining icing over top and sides of cake. Store loosely covered in refrigerator.