Preheat the oven to 325 degrees F (165 degrees C). Grease a 10-inch tube pan.

Combine flour and baking powder in a medium bowl; set aside. Combine milk and extracts in a liquid measure; set aside.

Cream sugar, butter, and shortening in a large bowl with an electric mixer until light and fluffy. Add eggs one at a time, beating well after each addition. Beat in flour mixture alternately with milk mixture in batches, beginning and ending with flour mixture. Spoon mixture into the prepared pan.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, 1 1/2 to 1 3/4 hours. Cool in the pan on a wire rack for 10 minutes.

While cake is cooling, make glaze: Combine sugar, water, and extracts in a saucepan. Bring to a boil, stirring until sugar is dissolved.

Turn cake out onto the wire rack. Place waxed paper under the rack to catch glaze drippings. Slowly spoon glaze over the top of hot cake. Cool completely.