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1
To make the cake: Heat oven to 325 degrees .
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2
Butter and flour a light-colored 10-inch fluted tube pan, making sure there are no clumps of butter or exposed areas in pan; set aside.
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3
Sift together flour, baking powder, and salt into large bowl and set aside.
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4
In the bowl of a standing mixer with a paddle set on medium speed, cream 3 sticks of butter until fluffy, about 2 minutes.
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5
Add the light brown and white sugars and mix, stopping and scraping down the bowl with a rubber spatula occasionally, until lightened and smooth, about 5 minutes.
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6
Reduce speed to medium-low and add eggs, one at a time, beating for about 15 seconds after each addition and scraping down the bowl occasionally, until well blended.
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7
Do not overmix.
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8
Reduce speed to low and add the flour mixture and 11/2 cups milk alternately, in 3 batches, beginning and ending with flour; beat until smooth, about 3 minutes total.
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9
Scrape the batter into the prepared pan and bake in the center of the oven until a wooden skewer inserted in the center comes out clean, about 1 hour and 10 minutes.
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10
Do not overbake.
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11
Let cake cool in the pan on a wire rack for at least 30 minutes.
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12
Loosen edges with a small knife, then turn onto rack to let cool completely.
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13
To make the icing: Melt remaining stick of butter in a large heavy saucepan over medium heat.
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14
Add dark brown sugar and whisk constantly until mixture is bubbling and smooth and butter is completely incorporated, about 3 minutes.
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15
Remove from heat and whisk in remaining 1/2 cup milk.
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16
Let mixture cool.
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17
Stir in the vanilla, then gradually add the confectioners' sugar and stir until well blended and smooth.
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18
Transfer cake to a cake plate and ice with frosting.
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19
Let stand for at least 2 hours before slicing.
