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For the cupcakes:
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1. Preheat your oven to 350 F.
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2. Line 1 standard size 12-count muffin tin with cupcake liners. This will make about 20 cupcakes, so you may need to bake in batches, or line 2 muffin tins.
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3. Whisk your flour, baking powder, baking soda, salt and cocoa powder together in a bowl.
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4. In a separate bowl, or in a stand mixer, add your butter and sugar and beat until light and fluffy.
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5. Add both of your eggs, mixing on low speed until smooth and combined.
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6. Pour your coke, rum and vanilla into the creamed mixture and mix them in. It is going to curdle, but when you add your dry ingredients, everything comes together.
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7. Slowly start to add your dry ingredients about 1/3 at a time. Mix with a spoon until all combined.
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8. Pour into cupcake liners in a muffin tin and fill each about 3/4 of the way full.
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9. Bake for 13-16 minutes. They are done when a toothpick inserted in the center of one comes out clean. Remove pan from oven and set on a rack to cool.
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10. Once they're cool, mix the glaze ingredients in a small bowl and then brush the tops of each cupcake, letting it soak in.
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For the frosting:
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1. Add the butter and vanilla into your mixer bowl and beat until smooth.
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2. Slowly add 1 cup of your powdered sugar and mix it in.
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3. Mix in your rum then mix in the rest of your powdered sugar. If it feels too wet, add a bit more powdered sugar. If it's a little dry, add very small drops of milk until it's just right.