Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.

In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.

In a large bowl, cream together the softened butter and granulated sugar until light and fluffy (about 3 minutes). Beat in the egg and vanilla extract until well combined.

Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Mix in the mashed peaches and milk until a soft, sticky dough forms.

Drop rounded tablespoons of dough onto the prepared baking sheets, leaving about 2 inches between each cookie.

Bake for 10-12 minutes, or until the edges are set but the centers remain soft. Let cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.

While cookies cool, prepare the glaze: Whisk together the powdered sugar, peach juice (or milk), and lemon zest until smooth. If too thick, add more liquid a half teaspoon at a time.

Once cookies are completely cool, drizzle or dip the tops with the peach glaze. Allow the glaze to set before serving.