Brown the butter. In your saucepan heat the butter over medium high heat for 3-4 minutes. Stir occasionally as it bubbles and becomes aromatic. Remove from the heat when it turns a deep amber. Pour the butter into a heat-safe bowl and store it in the fridge to cool for 10 minutes.
Preheat the oven to 350°F and position two racks equidistant from the center of the oven. Cover your baking sheets with parchment paper. Place the blueberries in a bowl and toss them with a pinch of flour (around a tablespoon) until they are all coated. Set aside.
Make the batter. Add the butter to a large bowl and stir in the brown sugar and granulated sugar. Add the eggs, vanilla extract and whisk together until the batter is shiny and smooth.
Add the flour, baking soda, cinnamon, baking powder and salt and stir until a dough forms. It will become pretty thick but malleable.
Form your cookies. Add the remaining ⅓ cup of granulated sugar to a small bowl. Using a ¼ cup measure, measure out a scoop of cookie dough and form it into a flat disc with your hands. Add about 4-5 blueberries to the center of the cookie. With your fingers, seal the blueberries inside the dough and roll the cookie into a firm ball. Roll the cookie in the granulated sugar and place it on a baking sheet. Repeat and place six cookies (spread out) on each baking sheet.
Bake the cookies. Place both sheets into the oven and bake them for 7 minutes. Then remove the cookie sheets, swap their positions in the oven (and rotate each pan), and bake them for 7 more minutes. Remove from the oven and let cool. Enjoy!