Preheat oven to 325°. Beat butter and shortening at medium speed with a heavy-duty electric stand mixer until creamy. Gradually add brown sugar, beating at medium speed until light and creamy. Add eggs, 1 at a time, beating just until blended after each addition.
Stir together evaporated milk and bourbon in a bowl. Stir together flour, baking powder, and salt in another bowl. Add flour mixture to butter mixture alternately with milk mixture, beginning and ending with flour mixture. Beat at low speed just until blended after each addition. Stir in vanilla bean paste. Pour batter into a greased and floured 10-inch (12-cup) Bundt pan.
Bake at 325° for 1 hour and 5 minutes to 1 hour and 10 minutes or until a long wooden pick inserted in center comes out clean. Cool in pan on a wire rack 10 to 15 minutes; remove from pan to wire rack. Cool completely (about 1 hour). Dust top lightly with powdered sugar.