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

Beat butter, brown sugar, and white sugar together with an electric mixer in a bowl until creamy and smooth, about 2 minutes. Add egg and vanilla extract; mix until incorporated.

Whisk flour, cinnamon, baking soda, baking powder, and salt in a separate bowl; mix into butter mixture until just combined. Fold in oats and blueberries.

Spoon dough, about 1 tablespoon per cookie, onto the prepared baking sheets about 2 inches apart.

Bake 1 sheet at a time in the preheated oven until cookies are golden brown, about 12 minutes. Transfer to a wire rack to cool completely.