In a small saucepan, cook the peaches, brown sugar, cinnamon, cornstarch, lemon juice, and ginger over medium heat for 4-5 minutes until thickened. Cool completely.
Preheat the oven to 350°F (175°C) and line a baking tray with parchment paper.
Beat the butter and dark brown sugar until creamy.
Mix in the egg and vanilla.
Stir in the flour, baking powder, and salt until a soft dough forms.
Divide the dough into 12 equal balls and place them on the prepared baking tray.
Press an indentation into the center of each cookie.
Spoon the cooled peach filling into each indentation.
Bake for 13-15 minutes until the edges are lightly golden.
Cool the cookies completely on a wire rack.
Whisk together the glaze ingredients until smooth.
Drizzle the glaze over the cooled cookies before serving.