Preheat the oven to 375 degrees. Grease an 8- by 2-inch round cake pan (or a 9-inch pan) and line with a parchment round. Grease and flour the parchment.
Beat in butter until fluffy. Beat in sugar. Beat in yolks and then peanut butter until smooth.
Mix the flour and baking powder in a bowl. Combine the buttermilk and water in another bowl and stir in the baking soda. Into the yolk mixture, beat in the flour mixture, in fourths, alternating with the buttermilk mixture and ending with the flour mixture.
Beat the egg whites until stiff. Fold into the batter with a rubber spatula. Spread the batter in a prepared pan. Bake for 30 to 40 minutes, until a wooden pick inserted into the center comes out clean. Cool the cake in a pan on a wire rack, about 10 minutes. Invert onto the rack; invert onto another rack, so that the cake cools with top side up. Serve warm or at room temperature. YIELD 8 to 10 servings.