Preheat and prep: Set the oven to 350°F (175°C).
Line two baking sheets with parchment paper.
Make the cookie dough: In a mixing bowl, beat the butter and sugar until light and fluffy, about 2 minutes. Add the egg and vanilla and beat until smooth.
Whisk dry ingredients: In a separate bowl, whisk the flour, baking powder, baking soda, and salt.
Combine: Add dry ingredients to the wet mixture in two additions, mixing just until combined. Stir in the milk to loosen the dough slightly.
The dough should be soft but not sticky.
Form the crunch topping: In a food processor, pulse the freeze-dried strawberries into small pieces (not a fine powder). Add the sandwich cookies and pulse into coarse crumbs. Toss with melted butter, sugar (if using), and a pinch of salt until it clumps slightly.
Shape the cookies: Scoop the dough into 2-tablespoon balls.
Gently press the tops of each ball into the strawberry crunch mixture, coating the top and sides.
Bake: Arrange 2 inches apart on the baking sheets, crunch-side up. Bake for 9–11 minutes, until the edges look set and the centers are slightly soft. Do not overbake.
Cool: Let the cookies rest on the sheet for 5 minutes, then transfer to a wire rack.
Glaze: Whisk powdered sugar, vanilla, salt, and just enough milk to make a thick, pourable glaze.
Drizzle over cooled cookies. Let set for 15–20 minutes.