Heat oven to 350°F. Spray pizza pan or cookie sheet with cooking spray or line with cooking parchment paper. Remove cookie dough from package; press into disk shape. On pizza pan, roll dough into round about 1/4 inch thick.
Bake 15 to 20 minutes or until lightly golden. Cool 15 minutes.
Meanwhile, in medium bowl, mix powdered sugar, 2 tablespoons milk and the vanilla. Stir in enough remaining milk, 1 teaspoon at a time, until icing is drizzling consistency. Spoon icing into small resealable food-storage plastic bag.
Spread blueberry pie filling over cookie. Cut off small corner of plastic bag; squeeze bag to pipe icing over filling. Sprinkle with brown sugar.
To serve, cut into wedges.