Begin by blending the freeze-dried strawberries into a fine powder.
Preheat oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a large bowl, cream together butter, sugar, and vanilla until light and fluffy. Beat in the egg until well incorporated.
Gradually mix in the flour, baking soda, a portion of the strawberry powder, and salt. Fold in the strawberry jam until the dough is well combined.
Roll the dough into small balls and arrange them on the prepared baking sheet. Bake for 8 minutes.
Lightly tap the baking sheet to flatten the cookies, then bake for an additional 2-3 minutes until the edges are set.
While cookies cool, prepare the icing. Blend together cream cheese, powdered sugar, hot milk, vanilla extract, and the remaining strawberry powder until smooth. Adjust the icing’s consistency with additional milk if needed.
Dip the cooled cookies in the icing or drizzle it over the top.