Preheat the oven to 375°F. Line 2 baking sheets with parchment paper or silpat mats.
MAKE THE COOKIE DOUGH:
In a large bowl, use an electric mixer to combine the butter and sugar. Beat in the egg and lemon extract. Gradually add the flour, alternating with the milk addition. Gently stir in the blueberries.
Drop the batter 1½ inches apart as rounded spoonfuls on the prepared baking sheets. (I use a cookie dough scoop.) Bake for 10 to 12 minutes. Let the cookies cool completely.
ADD THE GLAZE:
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.
Notes
Don't wash the blueberries! They tend to get soggy and will provide too much additional moisture to the cookie. If you absolutely must, rinse them lightly and let completely dry before using.