For the cakes
1 cup (2 sticks) butter, room temperature, plus more for pans
2 cups all-purpose flour, plus more for pans
2 teaspoons baking powder
1/2 teaspoon coarse salt
1/2 cup buttermilk
2 tablespoons dark rum
1 cup packed light brown sugar
1/2 cup granulated sugar
5 large eggs
For the glaze
2 cups confectioners’ sugar
1 tablespoon rum, plus up to 1 1/2 teaspoons more, if needed
1 tablespoon plus 1 1/2 teaspoons milk
1. Make the cakes: Preheat oven to 325°F. Generously butter nine 1-cup mini Bundt pans; dust with flour, tapping out excess. Sift together flour, baking powder, and salt into a medium bowl. Combine buttermilk and rum in a glass measuring cup.
2. With an electric mixer on high speed, beat butter, brown sugar, and granulated sugar until pale and fluffy, about 3 minutes. Reduce speed to medium. Add eggs, 1 at a time, beating well after each addition. Reduce speed to low. Add flour mixture in 2 batches, alternating with the buttermilk mixture and beginning and ending with the flour; beat until just combined.
3. Fill each pan with about 1/2 cup batter; tap pan on counter. Bake until tops spring back when lightly touched, edges begin to pull away from pan, and a cake tester comes out clean, 18 to 25 minutes. Transfer pans to a wire rack to cool 10 minutes; turn out cakes onto rack to cool completely. (Cakes can be stored at room temperature, wrapped in plastic, up to 3 days.)
4. Make the glaze: Whisk together confectioners’ sugar, 1 tablespoon rum, and milk until smooth, adding more rum if needed to reach desired consistency. Set cakes on a wire rack over a rimmed baking sheet. Drizzle 1 1/2 tablespoons glaze over each cake.
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