Melt the butter over medium-low heat. Add the brown sugar and stir well to dissolve. Let cool for a few minutes and transfer to a mixing bowl. Stir in the egg and vanilla.
Combine flour and baking powder and add to wet ingredients. Stir to combine. Fold in the nuts. Pour into a lightly buttered cake pan. Bake 20-25 minutes in preheated 350° F oven.
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