Preheat oven to 375°F (190°C). Line a baking sheet with parchment paper.
In a medium bowl, whisk together the flour, baking powder, and salt.
In a large bowl, cream together the butter and cream cheese until light and fluffy. Beat in the sugar until well combined.
Beat in the egg and vanilla extract until just combined.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Gently fold in the blueberries.
Cover the dough with plastic wrap and refrigerate for at least 30 minutes, or up to 2 hours.
Roll the dough out on a lightly floured surface to 1/4-inch thickness. Cut out the cookies with a 2-inch round cutter.
Place the cookies on the prepared baking sheet, leaving about 2 inches of space between each cookie.
Bake for 10-12 minutes, or until the edges are golden brown.
Let the cookies cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.