Preheat the oven to 350 degrees F (180°C)with oven rack in the center of oven.
Combine Wet Ingredients: Whisk the milk, sour cream and rum together in a liquid measure and let come to room temperature.
1/4 cup milk, 1/3 cup sour cream, 1/3 cup rum
Cream butter and sugar: In a large bowl or stand mixer whip the butter on medium speed for 1 minute. Add the granulated sugar and beat for 3-4 minutes until light and fluffy. Add vanilla. Add eggs and egg yolks, one at a time, mixing just between additions. Scrape down the sides of the bowl.
1 cup butter, 1 3/4 cups granulated sugar, 2 teaspoons vanilla extract, 3 large eggs, 2 large egg yolks
Mix Dry Ingredients: Combine the cake flour, baking powder, baking soda and salt.
Alternate Ingredients: Add 1/3 of the dry ingredients to the batter and mix just until combined. Add 1/2 of the milk/sour cream mixture and mix. Add another 1/3 of the dry ingredients, mixing just until combined. Add the last 1/2 of the milk/sour cream mixture and beat until just combined. Add the final 1/3 of the dry ingredients and mix just until combined, scraping down the sides of the bowl.
Bake: Grease and flour bundt pan. (I use shortening, and make sure every crevice of the pan is coated. The lightly dust with flour). Pour batter evenly into the pan and bake at 350 degrees F for about 50 minutes or until a toothpick inserted in the center comes out clean, or with few crumbs.
Glaze: Add glaze ingredients to a saucepan over medium heat. Stir well until butter has melted and mixture is smooth. Bring mixture to a boil, stirring, and boil for 2 minutes.
½ cup butter, 1/2 cup granulated sugar, ½ cup brown sugar, ¼ cup rum, ¼ cup heavy cream, 1 teaspoon vanilla extract
Finish Cake: Allow the cake to cool in the pan for 15 minutes before gently inverting it. (I like to remove the cake first, to make sure to get it out easily). Then wipe the pan clean and put the cake back in it. Poke holes all over the cake and gently pour most of the glaze over the cake, reserving just a little.
Serve: Allow the cake to soak up the glaze and then invert it onto a plate or serving platter. Spoon remaining glaze on top before serving.
Store leftover rum cake covered in the refrigerator.
Video
Notes
Make Ahead Instructions: Homemade rum cake can be made and kept in the refrigerator for up to 5 days. Enjoy warm (reheat slices in the microwave) or cold.Freezing Instructions: For best results freeze the baked rum cake without the glaze. Wrap in plastic wrap then aluminum foil and freeze for up to 3 months. Thaw cake completely, then make glaze, poke holes in cake and add glaze. Allow it to rest for at least 30 minutes before serving.