Preheat oven to 350°F. Prepare a baking sheet with parchment paper. Set aside.
To make cookies, in a large bowl, beat together sugar, butter and cream cheese until smooth. Scrape down sides of bowl. Add egg, lemon juice and zest. Beat until smooth.
In a medium bowl, combine flour, baking soda, corn starch, and salt. Add to wet ingredients and beat until just combined. Fold in blueberries.
Scoop about 2 tablespoons dough onto prepared baking sheet. Bake for 10-15 minutes, until cookies are just set. Let cool.
To make glaze, stir together powdered sugar, half & half, and lemon juice. Drizzle on top of cookies and enjoy!