To prepare the cake, coat 2 (8-inch) round cake pans with cooking spray, and line bottoms with wax paper. Coat wax paper with cooking spray, and dust with 2 teaspoons flour.
Combine the granulated sugar and 1/2 cup butter in a large bowl, and beat with a mixer at medium speed until well-blended (about 5 minutes). Add the eggs and egg white, 1 at a time, beating well after each addition; beat in 2 teaspoons vanilla. Lightly spoon 2 cups flour into dry measuring cups; level with a knife. Combine 2 cups flour, baking soda, and salt; stir well with a whisk. Add the flour mixture to the sugar mixture alternately with buttermilk, beginning and ending with flour mixture; beat well after each addition.
Pour the batter into prepared pans. Bake at 350° for 25 minutes or until a wooden pick inserted in center comes out clean. Cool in pans 10 minutes on a wire rack; remove from pans. Carefully peel off wax paper, and cool completely on wire rack.
To prepare the icing, combine the brown sugar and the next 4 ingredients (brown sugar through dash of 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. Pour brown sugar mixtureinto a large bowl. Add powdered sugar and 1 teaspoon vanilla; beat with a mixer at medium speed until smooth. Cool 2 to 3 minutes (icing will be thin but thickens as it cools).
Place 1 cake layer on a plate, and spoon 1/3 cup icing onto the cake layer, spreading to cover. Top with remaining cake layer. Spread remaining icing over top and sides of cake. Sprinkle top with pecans. Store cake loosely covered in refrigerator.