Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a mixing bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Set aside.
In a separate large bowl, use an electric mixer or whisk to cream the softened butter and granulated sugar together until light and fluffy, about 2-3 minutes.
Add the egg and vanilla extract to the butter mixture, mixing until well combined.
Gradually add the dry ingredient mixture to the wet mixture, mixing until just combined.
Gently fold the mashed raspberries into the cookie dough using a rubber spatula.
Use a cookie scoop or tablespoon to portion out the cookie dough onto the prepared baking sheet, leaving about 2 inches between each cookie.
Roll each dough ball in granulated sugar to coat and then flatten slightly with your palm.
Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden but the centers are still soft.
Remove from the oven and allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.