Preheat oven to 350°F (175°C).
Crush freeze-dried strawberries into a fine powder.
Cream butter and sugar until light and fluffy.
Add egg and vanilla extract, mix well.
Stir in strawberry powder, flour, baking soda, and salt.
Fold in strawberry jam until combined.
Drop spoonfuls of dough onto baking sheets.
Bake for 10-12 minutes until edges are lightly golden.
Cool cookies on a wire rack.
For the icing, whisk cream cheese, powdered sugar, hot milk, and vanilla extract until smooth.
Spread icing over cooled cookies.
Let icing set before serving.