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For the dry cake mix:
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1. In a large bowl, combine dry cake mix ingredients.
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2. On low speed, combine ingredients until the mixture is the consistency of sand, and all particles are generally the same size.
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3. This mix can be made ahead and stored for up to 3 months in the refrigerator.
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For the cake batter:
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1. Preheat oven to 325 F.
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2. Grease a large bundt pan (12-cup capacity).
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3. Sprinkle chopped nuts onto the bottom of the pan.
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4. Place dry cake mix, pudding mix, milk, eggs, rum, vegetable oil, and vanilla in a large bowl. Using an electric mixer, combine on slow speed until just mixed, about 30 seconds.
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5. Increase the mixing speed to medium and beat for 2-3 minutes, until the batter is smooth and cream-coloured. Scrape down the bowl halfway to make sure everything is well incorporated.
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6. Scrape the cake batter into the prepared bundt pan. Bake for about 55 minutes or until a wooden skewer inserted into the cake comes out clean.
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7. Remove the cake from the oven and place pan on a cooling rack while you make the buttered rum syrup.
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For the buttered rum syrup:
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1. Combine butter, water, and sugars in a small saucepan. Bring to a boil over high heat.
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2. Turn the heat down and simmer until sugar is dissolved and syrup thickens, about 5 minutes.
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3. Remove the pan from the heat and stir in the rum.
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4. While the cake is cooling in its tin, brush the cake with the syrup until the syrup is all used up.
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5. Let the cake cool completely before turning it out onto a platter. It's best if you let it sit for a few hours to fully absorb all the syrup.