Begin by processing the freeze-dried strawberries in a food processor or blender until they become a fine powder.

Preheat the oven to 350°F (175°C) and prepare a baking sheet by lining it with parchment paper.

In a large mixing bowl, beat the softened butter and granulated sugar together until the mixture is smooth. Add in the vanilla extract, followed by the egg, and beat until fully incorporated. Gradually mix in the flour, baking soda, 1/4 cup of the strawberry powder (reserving the rest for the icing), and kosher salt. Finally, blend in the strawberry jam.

Roll the dough into 1-tablespoon sized balls and place them 2 inches apart on the prepared baking sheet. Bake for 8 minutes, then rotate the sheet and gently tap it on the counter to flatten the cookies. Continue baking for an additional 2-3 minutes, or until the edges of the cookies are just beginning to set. Remove from the oven and allow the cookies to cool on the baking sheet, as they will continue to cook slightly from residual heat.

To prepare the icing, whisk together the cream cheese, powdered sugar, hot milk, and vanilla extract in a mixing bowl. Add the remaining strawberry powder and mix until smooth. If necessary, adjust the consistency by adding more milk.

For a decorative touch, dip each cookie into the icing and allow it to set. These cookies are equally delightful whether iced or served plain. Store them in an airtight container for up to 5 days.