In a medium microwave safe bowl, heat the frozen blueberries in 20 second increments, stirring after each time, until they are soft, liquidy and jammy. This took me about 2-2.5 minutes.
Set aside to cool. They will thicken more as they cool.
Slowly beat the cornstarch water mixture, milk, the cooled jammy blueberries (about 3 heaping tablespoons...you may have some left over) into the creamed butter and sugar. It will look magenta and chunky.
Slowly beat in the gluten free flour mixture a little at a time until just combined.
The dough will be super sticky and lavender. Keep the dough in the bowl, cover the top with plastic wrap and chill for at least 2.5 hours.