Preheat the oven to 350 degrees F (175 degrees C). Line 2 baking sheets with parchment paper.

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

Beat sugar and butter in a large bowl with an electric mixer until light and fluffy, about 2 minutes. Mix in egg, vanilla extract, and almond extract until well combined. Add in 1/3 of the flour mixture and stir until just combined. Stir in 1/2 of the sour cream. Continue alternating additions of the flour mixture and sour cream, beginning and ending with the flour mixture, stirring until just combined. Do not overmix. Gently fold in blueberries and frozen pieces of cream cheese.

Drop 1 1/2 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 before removing to a wire rack to cool completely.