Heat oven to 350°F. Grease 10-inch angel food (tube) cake pan with shortening; lightly flour. In medium bowl, mix flour, 1/4 cup cocoa, the baking powder and salt.
In large bowl, beat granulated sugar, 1 cup butter, the shortening and 1 teaspoon vanilla with electric mixer on medium speed until light and fluffy, scraping bowl occasionally. Add eggs, one at a time, beating well and scraping bowl after each addition. Alternately add flour mixture and milk to sugar mixture, beginning and ending with flour mixture, beating and scraping after each addition. Pour batter evenly into pan.
Bake 1 hour 10 minutes to 1 hour 25 minutes or until toothpick inserted in center comes out clean. Cool upright in pan 25 minutes. Place serving plate upside down over pan; turn plate and pan over. Remove pan. Cool completely, about 2 hours.
In 1-quart saucepan, mix 2 tablespoons cocoa, the water, corn syrup and 2 tablespoons butter. Cook over low heat, stirring constantly, until mixture thickens. Remove from heat. Beat in 1/4 teaspoon vanilla and the powdered sugar with spoon until smooth. Spread glaze over top of cooled cake, allowing some to run down sides.