Preheat the oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.

In a mixing bowl, combine flour, sugar, baking powder, and salt.

Add melted butter, eggs, and vanilla extract to the dry ingredients and mix until just combined.

Gently fold in the sliced peaches.

Pour the batter into the prepared cake pan and spread evenly.

Bake in the preheated oven for 30 minutes or until a toothpick inserted into the center comes out clean.

Allow the cake to cool in the pan for 10 minutes before transferring to a wire rack to cool completely.