Prepare the Filling: Melt butter in a saucepan, add blueberries, water, sugar, cornstarch, lemon juice, cinnamon, and salt. Bring to a gentle boil, then simmer until thickened. Let cool.
Assemble the Cookies: Roll out pie crust and cut rounds. Place filling on half the rounds, top with remaining rounds, press edges to seal. Crimp edges with a fork. Brush with egg wash, sprinkle with sugar.
Bake the Cookies: Preheat oven to 350℉, cut slits in the tops of the cookies, bake for 15-20 minutes until golden. Cool on a wire rack.
Serving and Storage: Serve warm or at room temperature. Store leftovers in an airtight container at room temperature for up to 3 days or freeze.