Whisk the flour, baking powder, and salt together in a large bowl. Set aside.

With a handheld or stand mixer fitted with a paddle or whisk attachment, beat the butter, granulated sugar, and brown sugar together on high speed until creamy, about 2 minutes. Scrape down the sides and up the bottom of the bowl as needed. With the mixer running on low speed, add the egg, vanilla extract, lemon zest, and lemon juice. Beat on medium-high speed until combined. Scrape down the sides and up the bottom of the bowl as needed. With the mixer running on low speed, slowly add the dry ingredients and milk. Beat everything just until incorporated. Do not overmix. Dough will be very creamy, sticky, and thick. With a spoon or silicone spatula, carefully fold blueberries into cookie dough. Handle with care because some may break a little. Cover dough tightly with aluminum foil or plastic wrap and chill in the refrigerator for 30-45 minutes and up to 2-3 days.

Preheat the oven to 350°F (177°C). Line two large baking sheets with parchment paper or silicone baking mats. (Always recommended for cookies.) Set aside.

Remove cookie dough from the refrigerator. Scoop cookie dough, about 1.5 Tablespoons each, and place 3 inches apart on the baking sheets. If desired, sprinkle each with a little coarse sugar. Gives the cookies an extra crunch. Bake for 15-16 minutes or until a cookie springs back when lightly poked with your finger. (That’s how I test them!)

Remove from the oven and allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely before glazing.

Whisk the confectioners’ sugar, lemon juice, and half-and-half together until smooth. Add more confectioners’ sugar to thicken or more lemon juice/half-and-half to thin, if desired. Spoon over cookies. If applied lightly, the glaze will set within a couple hours.

Glazed cookies will stay fresh covered at room temperature for 2 days or in the refrigerator for up to 1 week.