Preheat oven to 375. Lightly oil pan. In a medium bowl combine flour, baking powder and salt. Combine the butter and sugar in a large bowl. Beat with an electric mixer on medium speed until creamy. Add eggs, basil, lemon zest, and vanilla. Beat until blended. Add the flour mixture, a third at a time, alternating with the buttermilk and beating on low speed until smooth. Pour into the oiled pan. Bake for 35 to 45 minutes, or until a wooden pick inserted in the center comes out clean. Let cake cool before taking it out of the pan.
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