Preheat your oven to 350°F (175°C). Grease and flour a 9-inch cake pan.
In a mixing bowl, whisk together the flour, sugar, baking powder, baking soda, and salt.
Add the softened butter and mix until the mixture resembles coarse crumbs.
In another bowl, beat the eggs, then add the vanilla extract and sour cream. Mix well.
Combine the wet ingredients with the dry ingredients, mixing just until combined.
Fold in the sliced peaches gently.
Pour the batter into the prepared cake pan and spread it evenly.
Bake for 45 minutes or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.