Preheat oven to 350°F.
In a large bowl, cream together the softened butter and granulated sugar until light and fluffy. Beat in the vanilla and egg white until well incorporated.
In a separate bowl, whisk together the flour and baking powder. Gradually mix the dry ingredients into the wet ingredients until a soft dough forms.
On a lightly floured surface, roll the dough out to 1/4 - 1/2 inch thickness. Use a 2 1/2 inch round cookie cutter to cut out circles and transfer them to an ungreased baking sheet, spacing about 1 inch apart.
Bake for 6-8 minutes, until the cookies are puffed and no longer glossy on top. Remove from oven and allow cookies to cool completely on the baking sheet.
While the cookies cool, make the caramel filling. Combine the unwrapped caramels and 1 tbsp milk in a microwave-safe bowl. Microwave for 1 minute, stirring at the 30 second mark. Stir until completely melted and smooth.
Once cookies are cooled, spoon about 1 tsp of the melted caramel into the center of each cookie, spreading it almost to the edges.
Transfer the caramel-topped cookies to the refrigerator and chill for 10-15 minutes to allow the caramel to firm up slightly.
Melt the milk chocolate chips in a microwave-safe bowl in 30 second increments, stirring between each, until completely melted and smooth.
Remove cookies from fridge and spoon a layer of the melted chocolate over the caramel centers, spreading to the edges.
Allow chocolate to set completely at room temperature before serving, about 20 minutes. Or return to fridge to set chocolate faster.