In a mixing bowl, cream together the butter and sugar until light and fluffy.

Beat in the egg and vanilla extract.

In a separate bowl, combine flour and baking powder, then gradually add to the wet mixture.

Chill the dough for 30 minutes.

Preheat the oven to 350°F (175°C).

Roll out the dough and cut into desired shapes using a cookie cutter.

Place half of the shapes on a baking sheet and add a spoonful of peach preserves to the center.

Top with the remaining shapes and seal the edges.

Bake for 15 minutes or until golden brown.

In a small bowl, mix together powdered sugar, milk, and vanilla extract until smooth.

Drizzle the glaze over the cooled cookies.