Line cupcake pans with cupcake liners. Stir together first 4 ingredients. Beat eggs and next 4 ingredients at medium speed with an electric mixer until smooth. Add flour mixture, beating at low speed until blended. Fold in carrot and next 3 ingredients. Pour batter into prepared cupcake pans. Bake at 350° for 25 to 30 minutes or until a wooden pick inserted in center comes out clean. Drizzle Buttermilk Glaze evenly over cupcakes; cool in pans on wire racks 15 minutes. Remove from pans, and cool completely on wire racks.
Southern Buttermilk Glaze
Bring first 5 ingredients to a boil in a large Dutch oven over medium-high heat. Boil, stirring often, 4 minutes. Remove from heat, and stir in vanilla.
Vegetable cooking spray
Line cupcake pan with liners, or coat each holder with vegetable spray.
Combine 3 cups flour and next 4 ingredients in a large bowl. Stir together eggs, applesauce, and oil; add to flour mixture, stirring just until dry ingredients are moistened. (Do not beat.) Stir in mashed banana, vanilla extract, and pineapple. Pour batter evenly into each cupcake holder about 3/4 full.
Bake at 350° for 23 to 25 minutes or until a wooden pick inserted in center comes out clean. Cool in pan on wire racks 10 minutes. Remove cupcakes from pan; cool completely on wire racks.