Step 1

Prepare the Cake: Preheat oven to 350°F. Generously coat a 10-inch (10- to 15-cup) Bundt pan with cooking spray; set aside. Stir together flour, baking powder, baking soda, and salt in a bowl; set aside.

Step 2

Beat butter, sugar, and vanilla in a stand mixer fitted with a paddle attachment on medium speed until light and fluffy, about 4 minutes. Add eggs, 1 at a time, and egg yolk, beating well after each addition. Reduce mixer speed to low; gradually beat in rum. Add flour mixture to egg mixture in thirds, alternately with heavy cream, beginning and ending with flour mixture, beating on low after each addition.

Step 3

Transfer batter to prepared Bundt pan, smoothing the top. Bake in preheated oven until golden brown and a wooden pick inserted in center comes out clean, 50 to 55 minutes (cover loosely with aluminum foil after 30 minutes to prevent excess browning, if needed). Remove from oven.

Step 4

During final 10 minutes of bake time, prepare the Rum Syrup: Melt butter in a saucepan over medium. Add sugar and ¼ cup water; let mixture come to a boil. Boil, stirring occasionally, until syrupy, about 5 minutes. Carefully add rum and vanilla. (Mixture will bubble.) Boil, stirring often, 1 minute. Remove from heat.

Step 5

Using a wooden skewer, poke warm cake in pan all over. Spoon ¾ cup of the Rum Syrup evenly over cake. Let stand 10 minutes. Invert onto a cake stand. Spoon remaining Rum Syrup (about ½ cup) evenly over top. Let cool at least 20 minutes or up to 8 hours before serving.