Prepare the oven: Line two baking sheets with parchment paper and heat the oven to 350°F.
Cream the butter mixture: Beat the softened butter, cream cheese, granulated sugar, and brown sugar until creamy and slightly fluffy.
Add the wet ingredients: Mix in the egg, vanilla, lemon zest, and lemon juice until evenly blended.
Combine the dry ingredients: Whisk together the flour, baking powder, baking soda, and salt. Add to the wet mixture in two additions, mixing gently until just combined.
Add the fillings: Fold in the white chocolate chips, followed by the blueberries. Handle the berries gently to prevent crushing.
Shape and chill: Scoop two tablespoons of dough per cookie, arrange on the baking sheets, and chill for 30 minutes.
Bake: Bake for 11 to 14 minutes, until the edges are set and the centers remain slightly soft.
Cool: Leave the cookies on the baking sheet for 8 minutes, then transfer them to a wire rack to cool completely.