Preheat oven to 375°F. Line a muffin tin, or lightly grease and flour a 9-inch round or 8-inch square cake pan. Sift together the flour, baking powder, baking soda, and sugar into a bowl. In a measuring cup, mix together the peach puree, oil and vanilla. Add the peach mixture to the dry ingredients and whisk together until combined. At this point, you may want to add some yellow and food colouring to achieve a peachier colour. When the batter is smooth, add the vinegar and stir quickly. The batter will foam slightly where the baking soda and vinegar are reacting. Stir just until the vinegar is evenly distributed throughout the batter. Pour the batter into the prepared pan, and bake for 20 minutes if making cupcakes, or 25 to 30 minutes it making cake. Allow to cool before glazing or frosting.
Peach Buttercream
Whip the butter until light and fluffy. Add the sugar and beat until well combined. Add peach puree and vanilla and beat again until smooth. You may want to add some yellow and red food colouring to achieve a peachier colour.