Prepare the Blueberry Filling:

1. In a small saucepan, combine 1 cup of fresh blueberries, 2 tablespoons of granulated sugar, 1 tablespoon of cornstarch, and 1 tablespoon of water.
2. Cook over medium heat, stirring constantly, until the mixture thickens and the blueberries start to break down. This should take about 5-7 minutes.
3. Remove from heat and let the filling cool completely.

Make the Cookie Dough:

1. In a medium bowl, whisk together 1 ½ cups of all-purpose flour, ½ teaspoon of baking powder, and ¼ teaspoon of salt. Set aside.
2. In a large bowl, beat ½ cup of softened unsalted butter and ½ cup of granulated sugar together until light and fluffy, about 3-4 minutes.
3. Add 1 large egg, 1 teaspoon of vanilla extract, 1 tablespoon of lemon zest, and 2 tablespoons of fresh lemon juice. Beat until fully combined.
4. Gradually add the dry ingredients to the wet ingredients, mixing until just combined. The dough will be soft and slightly sticky.

Assemble the Cookies:

1. Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
2. Scoop about 1 tablespoon of dough and flatten it slightly with your fingers.
3. Place about 1 teaspoon of the cooled blueberry filling in the center of the dough.
4. Scoop another tablespoon of dough, flatten it, and place it on top of the filling, sealing the edges gently with your fingers. Repeat with the remaining dough and filling.

Bake the Cookies:

1. Place the assembled cookies on the prepared baking sheet, spacing them about 2 inches apart.
2. Bake in the preheated oven for 12-15 minutes, or until the edges are lightly golden.
3. Remove from the oven and let the cookies cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.

Prepare the Lemon Frosting:

1. In a medium bowl, whisk together 1 ½ cups of powdered sugar, 2-3 tablespoons of fresh lemon juice, 1 tablespoon of milk, and ½ teaspoon of vanilla extract until smooth and slightly thickened.
2. If the frosting is too thick, add a little more lemon juice or milk until you reach your desired consistency.

Frost and Decorate the Cookies:

1. Once the cookies are completely cool, spread the lemon frosting on top of each cookie using a spoon or spatula.
2. Garnish with fresh blueberries on top of the frosting.
3. Allow the frosting to set for about 10 minutes before serving.