Preheat the oven to 350°F (175°C).
In a medium bowl, combine the flour, baking powder, baking soda, and salt. Mix well.
In a large bowl, beat the softened butter and granulated sugar together until light and fluffy.
Add the egg and vanilla extract, mixing until well combined.
Gradually add the dry ingredient mixture to the wet ingredients, mixing until just combined.
Gently fold in the blueberries, being careful not to break them.
Cover the dough and chill in the refrigerator for at least 30 minutes.
Scoop the dough using a tablespoon and roll it into balls. Roll each ball in powdered sugar until fully coated.
Place the dough balls on a baking sheet lined with parchment paper, spacing them about 2 inches apart.
Bake for 10-12 minutes, or until the edges are set but the centers still look slightly soft.
Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.