Preheat the oven to 350 degrees F. Line a baking sheet with parchment paper.
Add the cream cheese to a large mixing bowl. Beat with a hand mixer on medium until combined. Scrape down the sides of the bowl.
Add in the butter, granulated sugar, and powdered sugar. Beat until the butter is creamed and the sugars are combined.
Add in the vanilla extract, lemon juice, lemon zest, and egg. Beat just until the egg is incorporated.
Add in the flour, baking soda, and salt. Beat until the flour is just combined.
Fold in the frozen blueberries.
Cover the dough and refrigerate for at least 1 hour.
Using a 1 tablespoon cookie scoop, scoop the dough onto the prepared baking sheet.
Place into the preheated oven and bake for 10 to 13 minutes until the edges are golden brown.
Let cool for 5 to 10 minutes on the baking sheet before transferring to a cooling rack or paper towel to cool completely.
Glaze
In a medium bowl, add in the cream cheese. Using a hand mixer, beat on medium until creamy.
Add in the powdered sugar, milk, and vanilla extract. Beat until smooth.
If the glaze is too thick, add additional heavy cream 1 tablespoon at a time until you reach the desired consistency.
Dip the tops of the cooled cookies in the glaze. You can also add the glaze to a sandwich bag and cut the corner off from the bag creating a small hole. Drizzle the glaze on top of the cookies.
Place in an airtight container in the fridge for up to 5 days.
Notes
For a smooth cookie top, roll the chilled scoops of cookie dough into a ball. You may need to lightly grease your hands if the dough is sticking.