Preheat the oven to 350°F. Line 2 baking sheets with parchment paper and lightly spray with nonstick spray. Set them aside.
In a medium-sized mixing bowl, whisk together the flour, baking powder, baking soda, and salt. Set it aside.
Using a stand mixer or a medium-sized mixing bowl and a handheld mixer on medium-high speed, cream the butter, cream cheese, and granulated sugar for 1 to 1½ minutes.
Add the sour cream, egg, and vanilla extract. Mix until completely combined.
Lower the mixer speed to low, and add in the flour mixture. Mix just until the dry ingredients are well incorporated. Do not overmix.
Fold in the white chocolate chips and the blueberries.
Using either a 1 to 1½ tablespoon cookie scoop, scoop out the cookie dough. Space the dough 2 inches apart. Bake for 12 to 14 minutes, until the edges are golden.
Allow the cookies to cool on the cookie sheet for 5 to 8 minutes before moving to a cooling rack.