Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, cream the softened butter and granulated sugar together until light and fluffy, about 2-3 minutes.
Beat in the egg, lemon zest, lemon juice, and vanilla extract until well combined.
Gradually add the dry ingredients to the wet mixture, mixing until just combined. Be careful not to overmix.
Gently fold in the raspberries, being careful not to break them up too much.
Drop tablespoon-sized portions of dough onto the prepared baking sheet, spacing them about 2 inches apart.
Bake for 10-12 minutes, or until the edges are lightly golden. Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.
If desired, dust the cooled cookies with powdered sugar before serving.