Preheat oven to 325 degrees. Beat butter at medium speed with a mixer until creamy; gradually add sugar, beating until light and fluffy. Add eggs, 1 at a time, beating just until blended after each addition.
Stir together flour, apple pie spice, baking powder and salt. Add flour mixture to butter mixture, alternating with apple cider and mixing on low speed after each addition. Stir in vanilla.
Butter or spray a 12-cup mini Bundt pan with nonstick cooking spray. Pour batter into mold. Recipe makes 24 mini Bundt cakes, so you will make one batch, cool the pan and repeat. Bake 20 minutes or until toothpick inserted in center comes out clean. Cool in pan on wire rack 10 minutes, then remove from pan to rack, and cool completely.
In a heavy saucepan over medium-high heat, add sugar, apple spice, baking soda, buttermilk, butter and corn syrup, stirring and bringing to a boil. Remove from heat, and stir in vanilla.
Drizzle Buttermilk Glaze on cooled cakes.