Preheat the oven to 350º Fahrenheit. Grease with shortening and then dust with flour a 2 ½ quart bundt cake pan.
In a medium bowl, mix together the eggs, sugar, vanilla, orange juice and zest, oil and sour cream. Mix well until it is all incorporated.
In a small bowl, whisk together the flour and baking powder.
Add the dry ingredients to the wet ingredients and mix just until combined, scraping the sides of the bowl as needed.
Pour the batter into the prepared pan. Tap the pan a few times on the counter to release any air bubbles.
Bake the cake for 30 minutes.
Make the syrup:
While the cake is baking, prepare the syrup. In a small saucepan, heat the orange juice and sugar together. Bring to a low boil and boil for 1 minute to allow the sugar to dissolve. Then remove from the heat.
As soon as the cake comes out from the oven, poke holes into the top of the cake with a thin sharp knife, long skewer, or long fork.
Slowly drizzle the hot rum soak over the top of the cake while it is still in the pan. It will mostly go to the outside of the cake and that’s ok because it will soak down and soak into the top of the cake.
Once the syrup has totally soaked into the cake (give it about 5-10 minutes), invert to a wire rack to cool completely.
Loosen the sides of the cake from the pan with a butter knife or a rubber spatula. Jiggle the pan slightly to loosen the cake.
Turn the cake out onto a cake plate.
Make the glaze:
As the cakes cool, prepare the glaze.
Whisk together the powdered sugar and 1 tablespoon of orange juice until smooth. Add a second or third tablespoon if needed to get a drizzling consistency.
Drizzle the glaze over the cooled cake.
The calories shown are based on the cake being cut into 15 pieces, with 1 serving being 1 slice of cake. Since different brands of ingredients have different nutritional information, the calories shown are just an estimate. **We are not dietitians and recommend you seek a nutritionist for exact nutritional information.*****This cake can be made with a slightly smaller cake pan. It is a short cake so should not bake over.