Preheat your oven to 350 degrees F. Line a baking sheet with parchment paper. Set aside
In a medium mixing bowl, stir together the flour, baking powder, baking soda, and salt. Set aside
In the bowl of a stand mixer fitted with the paddle attachment, mix the butter, sugar, and lemon zest until smooth and fluffy, about 1-2 minutes. Add the egg, vanilla, and lemon juice and mix to combine.
Add the dry ingredients to the wet ingredients in 3 additions, mixing until just combined after each addition.
Gently stir in the raspberries with a rubber spatula until evenly distributed.
Carefully scoop the cookie dough using a medium cookie scoop (about 2 tablespoons) onto the prepared baking sheet. Leave about 2 inches between the cookies as they will spread.
Bake for 12-15 minutes or until the cookies are just turning golden around the edges and they're no longer glossy on top.
Remove from the oven and allow to cool on the baking sheet for 5 minutes. Then transfer the cookies to a wire rack to cool completely.
Mix together the powdered sugar and lemon juice in a medium mixing bowl until your desired glaze consistency is reached. (see note) Drizzle lemon glaze over the cooled cookies before serving.
Notes
The raspberries must be frozen otherwise they will break too small when mixing them into the dough. This also helps prevent the color from bleeding into the cookies too much.
The cookie dough will seem a little drier than other cookie doughs, but it's okay because the raspberries have lots of moisture in them that they release while baking.
If the glaze is too thick, add a little more lemon juice and mix. If it's too thin, add more powdered sugar (1 TBSP at a time) until thickened to your liking.
Store leftovers in an airtight container for 2-3 days on the counter, 3-4 days in the fridge, or 2-3 months in the freezer.