In a medium mixing bowl, whisk together the flour, salt, and baking powder until evenly combined. Set aside.

In a large mixer-safe bowl, combine the room temperature butter and granulated sugar. Using an electric mixer, beat the mixture on medium speed until well combined and smooth, about 2–3 minutes.

In a small bowl, whisk together the cornstarch and water until fully combined and smooth. Set aside.

To the butter and sugar mixture, add the milk, lemon zest, and fresh lemon juice. Mix until fully incorporated.

Gradually add the prepared flour mixture to the wet ingredients, mixing until a soft dough forms. Add the cornstarch slurry and mix until incorporated. If desired, add a few drops of lemon extract and purple food coloring for additional flavor and color.

Using a rubber spatula, gently fold in the frozen blueberries, mixing just until evenly distributed.

Cover the bowl with plastic wrap and place the dough in the refrigerator for 1½ hours to allow it to firm up.

In a small bowl, combine the granulated sugar, dried lavender, and lemon zest (if using). Mix well and set aside.

While the dough chills, prepare the glaze. In a small saucepan over low heat, combine the blueberries and water. Cook while gently stirring and mashing the berries until they soften and begin to form a jam-like consistency with small chunks remaining. Remove from heat and allow the mixture to cool completely. In a bowl, whisk together the confectioners’ sugar, cooled blueberry mixture, a squeeze of lemon juice, and a small amount of water until a smooth glaze forms. Adjust the consistency as needed. Set aside.

Preheat the oven to 325°F (163°C). Line a baking sheet with parchment paper and lightly grease with cooking spray or oil.

Using a cookie scoop or spoon, portion the dough into balls. Roll each dough ball in the lavender sugar mixture until fully coated. Place the coated dough balls on the prepared baking sheet, leaving space between each cookie. Gently press down on each cookie to flatten slightly to help achieve a chewy texture.

Bake for 17 minutes, or until the edges are set.

For a more uniform shape, place a wide mug or glass over each warm cookie and gently swirl it around to create a more rounded edge. This step is optional. Allow the cookies to cool completely on a wire rack.

Once the cookies are fully cooled, drizzle the blueberry glaze over the tops. If desired, sprinkle with a small amount of additional lavender sugar and sprinkle salt. Serve and enjoy.