Preheat oven to 350ļ
Grease a 10-15 c bundt pan with cooking spray.
Stir together flour, baking powder, baking soda and salt in a bowl.
In a large bowl, beT 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 , one 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.
Transfer batter to pan, smoothing the top. Bake 50-55 minutes until golden(cover loosely with foil after 30 minutes to prevent excess browning if needed) brown and a wooden pick inserted in center comes out clean.
Remove from oven.
During last 10 minutes of baking time prepare the rum syrup. Melt butter in a saucepan over medium heat. Add sugar and 1/4 c 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 for 1 minute. Remove from heat.
Using a wooden skewer, poke holes in bake in pan all over. Spoon 3/4 c of the rum syrup evenly over cake. Let stand 10 minutes. Invert onto cake stand. Spoon remaining rum syrup ( about 1/2 c) evenly over the top. Let cool at least 20 minutes or up to 8 hours before serving.