Preheat oven to 350°F (175°C) and line baking sheets with parchment paper.
In a medium bowl, whisk together flour, baking powder, and salt.
In a large bowl, beat butter and sugar until light and fluffy.
Add eggs one at a time, mixing well after each addition.
Mix in vanilla extract and milk.
Gradually add dry ingredients and mix until soft dough forms.
Roll dough into small balls and place on prepared baking sheets. Flatten slightly.
Bake for 10–12 minutes until bottoms are lightly golden. Cool completely.
Spread peach preserves onto one cookie half and add small amount of diced peaches. Top with another cookie to form sandwich cookies.
In a small bowl, whisk powdered sugar, milk or peach juice, and vanilla until smooth.
Drizzle or spread glaze over cookies and decorate if desired.
Allow glaze to set before serving.