Preheat the oven to 350℉ (175℃). Line 2 baking sheets with parchment paper; set aside.

Whisk together flour, baking powder, baking soda, and salt in a medium bowl. Set aside.

Beat the sugar, cream cheese, and butter in a large bowl with an electric mixer until light and fluffy, about 2 minutes. Mix in the egg, vanilla extract, and sour cream until well combined.

Add the flour mixture and stir until just combined. Do not overmix.

Gently fold in the blueberries. Drop 1½ tablespoon-sized balls of dough onto the prepared baking sheets about 2 inches apart.

Bake in the preheated oven until the bottom of the cookies just begins to brown, 15 to 18 minutes. Cool on the baking sheets for 5 minutes, then transfer to a wire rack to cool completely.