Cream butter and powdered sugar in a mixing bowl until light and fluffy, about 2-3 minutes. Add vanilla extract and mix just until combined.

Gradually add all-purpose flour to the butter mixture, mixing on low speed until just combined, ensuring not to overmix.

Crush freeze-dried strawberries into a fine powder and gently fold into the cookie dough until evenly distributed.

Transfer the dough to a floured surface, knead gently until it holds together, roll into a log, and wrap in plastic wrap. Refrigerate for 30 minutes.

Preheat the oven to 325°F (160°C). Slice the chilled dough into rounds, place on parchment-lined baking sheets, and bake for 18-22 minutes until edges are lightly golden.

Let cookies rest on the sheet for 5 minutes before transferring to a wire rack to cool completely.

In a small bowl, whisk powdered sugar with milk until smooth. Adjust consistency with more milk if needed.

Drizzle or dip cooled cookies into the glaze, allowing excess glaze to drip off, and let set for 10-15 minutes.