Preheat oven to 350 degrees F, and line an 8×8 baking dish with parchment paper. Grease the sides that aren't covered.
Place the freeze dried strawberries in a food processor or coffee grinder, and grind until it's mostly fine and powdery. It should reduce to about 1/2 cup. Place in the fridge until ready to use - it will clump at room temperature if it's too humid.
If the butter is cold, cut the butter in cubes and place in a large mixing bowl. Chop white chocolate into smaller pieces and add to the bowl. Microwave for 30 seconds at a time (use a glass bowl for the microwave), or use a double boiler until the butter is melted and the white chocolate pieces are softened. Remove from heat and stir until melted together.
Add milk, sugar, salt, and vanilla extract and whisk together. You can add food coloring here, if using.
Whisk in eggs until smooth.
Reserve 1 tbsp of powdered freeze dried strawberries for the icing and add the rest to the batter, along with flour. Fold in until just combined. Don't over-mix.
Pour into the prepared baking sheet, spreading evenly. Bake for 25-30 minutes, until light browned on the edges and set in the middle. The middle may seem a bit soft, but it'll firm up as it cools.
Cool for 5 minutes, then use the parchment paper to carefully remove the brownies from the baking dish. Cool completely.
Once the brownies are cooled, stir together powdered sugar, milk, and the reserved powdered freeze dried strawberries in a bowl. Add a little more milk if the mixture is too thick. You want it thick but spreadable, but not too runny.
Pour the icing on top of the brownies and smooth it out using a spatula. You can top with some crushed freeze dried strawberries if you want - I just broke them up with my fingers.
Once the icing sets, cut into 16 squares. Enjoy!