Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a large bowl, cream together the softened butter, granulated sugar, and light brown sugar until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
In a separate bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the lemon zest, sour cream, and fresh blueberries gently to avoid breaking the berries.
Using a cookie scoop or spoon, drop heaping tablespoons of dough onto the prepared baking sheets, spacing them about 2 inches apart. Flatten each mound slightly with the back of the spoon to form muffin-top shapes.
Bake in the preheated oven for 10-12 minutes, or until the edges are golden and the centers are set but still soft.
Remove from the oven and allow the cookies to cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.