Step 1: Preheat oven to 375°F (190°C). Line two baking sheets with parchment paper or silicone baking mats for easy release and cleanup.
Step 2: In a medium bowl, whisk together the all-purpose flour, baking powder, and salt until thoroughly combined. Set aside.
Step 3: In a large bowl, using an electric mixer (stand or hand mixer), cream together the softened unsalted butter and granulated sugar until light and fluffy, about 2-3 minutes.
Step 4: Beat in the large egg and vanilla extract until just combined, scraping down the sides of the bowl as needed.
Step 5: Add the lemon zest and 2 tablespoons of fresh lemon juice to the wet ingredients, mixing until well incorporated and fragrant.
Step 6: Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Be careful not to overmix the dough.
Step 7: Gently fold in the fresh raspberries using a spatula, being very careful not to crush them to avoid bleeding and excess moisture.
Step 8: Cover the dough tightly with plastic wrap and chill it in the refrigerator for at least 30 minutes. This is crucial for preventing the cookies from spreading too much during baking.
Step 9: Drop rounded tablespoons of dough onto the prepared baking sheets, leaving about 2 inches between each cookie for even baking and slight spread.
Step 10: Bake for 10-12 minutes, or until the edges are lightly golden and the centers are just set. They may appear slightly underdone in the middle, but will firm up as they cool.
Step 11: Let the cookies cool on the baking sheets for 5 minutes before carefully transferring them to a wire rack to cool completely.
Step 12: (Optional Glaze) While cookies cool, whisk together the powdered sugar and 1-2 tablespoons of fresh lemon juice in a small bowl until smooth. Adjust consistency with more lemon juice or powdered sugar as needed.
Step 13: Once the cookies are completely cool, drizzle them with the lemon glaze. Allow the glaze to set for about 15-20 minutes before serving.