Preheat oven to 350°F. Line 2 baking sheets with parchment paper.
In a large bowl, beat butter, granulated sugar, and brown sugar until light and fluffy, about 2 minutes.
Beat in the egg, lemon zest, lemon juice, and vanilla until smooth.
Whisk flour, baking powder, baking soda, and salt in a separate bowl. Add to the wet mixture and mix on low just until combined; do not overmix.
Fold in freeze-dried raspberries and white chocolate chips (if using).
Scoop dough into 1.5-tablespoon portions, spacing about 2 inches apart on baking sheets.
Bake 9 to 11 minutes, until edges are set and centers look slightly soft. Do not overbake.
Cool on the sheet for 5 minutes, then transfer cookies to a wire rack to cool completely.
Whisk powdered sugar with lemon juice, adding milk as needed for a thick drizzle. Glaze cooled cookies and let set for 15 minutes.
Notes
For the prettiest look, lightly crush freeze-dried raspberries so they distribute color without bleeding. Store cookies in an airtight container at room temperature for up to 3 days or freeze (unglazed) for up to 2 months.