In a large bowl, use an electric mixer to combine the sugar and butter. Beat in the egg and lemon extract.
Gradually add flour, alternating with milk addition.
Carefully stir in the blueberries and drop the batter 1½-inches apart on greased cookie sheet, silpat-mat or parchment lined baking sheet. I use a cookie dough scoop.
Bake 10-12 minutes.
ADD THE GLAZE:
Let the cookies cool completely. In a small bowl, whisk together the powdered sugar and lemon juice. Drizzle each cookie with a little bit of the lemon glaze. The glaze will set when it has a chance to dry.