Preheat your oven to 350°F (175°C) and prepare a 9-inch round cake pan by greasing it with butter or non-stick spray.

In a medium mixing bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt until well blended.

In a large mixing bowl, cream the softened unsalted butter and granulated sugar together until the mixture is light and fluffy, about 3-4 minutes.

Add the eggs one at a time to the butter-sugar mixture, mixing well after each addition, then stir in the vanilla extract.

Gradually add the whisked dry ingredients to the butter mixture, alternating with the buttermilk, and mix just until combined.

Chop the fresh peaches into small pieces and toss them in a little flour before folding into the batter.

Pour the batter into the prepared cake pan, smoothing the top with a spatula.

Bake for 40-45 minutes, or until the edges are golden brown and a toothpick inserted comes out clean.

Allow the cake to cool in the pan for about 10 minutes, then let it cool completely on a wire rack.