Preheat your oven to 350 degrees. In a medium bowl, whisk together the flour, powdered strawberries, baking soda, cream of tartar, and salt. Set aside.
In a large bowl, beat together the butter and sugar until light and fluffy. Add in the egg yolks, vanilla extract, and beat until combined. Slowly add in the flour mixture and beat until fully combined.
Scoop out dough in 2-tablespoonfuls and place on a lined baking sheet about 2 inches apart. Bake for 12-13 minutes, or until cookies just begin to brown on the edges- do not over bake! They should be puffy and cracked all over, and they will settle as they cool.
For the frosting:
In a medium bowl, beat together the softened butter, powdered sugar, and powdered freeze dried strawberries until combined and very thick. The mixture may be a little clumpy at this point. Add in the salt and melted white chocolate, and beat until a thick frosting forms. Optionally, add in 1-2 tbs. milk as needed to reach your desired consistency.