To prepare cake, lightly spoon flour into dry measuring cups; level with a knife. Combine flour and next 5 ingredients (through salt) in a large bowl; stir with a whisk.
Combine 1 cup sugar, butter, and oil in a large bowl; beat with a mixer at medium speed until light and fluffy (about 5 minutes). Add eggs, 1 at a time, beating well after each addition. Combine buttermilk and 1 cup cider in a small bowl. Add flour mixture and cider mixture alternately to sugar mixture, beginning and ending with flour mixture. Stir in vanilla. Pour into a Bundt pan coated with cooking spray. Bake at 350° for 45 minutes or until a wooden pick inserted in center comes out clean. Cool in pan 10 minutes on a wire rack; remove from pan. Cool completely on wire rack.
To prepare glaze, combine 1 cup cider and 1 teaspoon sugar in a small saucepan over medium-low heat; bring to a simmer. Cook until reduced to 1/4 cup (about 15 minutes). Drizzle glaze over each serving of cake.