Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a medium bowl, whisk together the flour, baking powder, and salt.
In a large mixing bowl, beat the softened butter and granulated sugar until light and fluffy, about 3 to 4 minutes.
Add the egg and vanilla extract, mixing until fully combined.
Gradually add the dry ingredients into the wet mixture, stirring gently until just combined.
Fold in the diced fresh peaches carefully to avoid crushing them.
Scoop rounded portions of dough onto the prepared baking sheet, spacing the cookies about 2 inches apart.
Bake the Italian Peach Summer Cookies for 18 to 20 minutes or until lightly golden around the edges.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack.
Dust generously with powdered sugar before serving.