Preheat oven to 400°F. Line a muffin pan with paper liners or grease with butter.
In a small saucepan, cook the butter over medium low heat until browned, swirling the pan as needed to promote even cooking. Set aside to cool.
In a bowl, sift together the flour, baking powder, baking soda, and salt.
In a large bowl, combine the browned butter, ¾ cup sugar, and buttermilk. Whisk in the eggs and vanilla extract until smooth. Add the dry ingredients and stir until just combined. Fold in the blueberries.
Spoon the batter into the prepared muffin, filling each cup ¾ full. Sprinkle the remaining 2 tablespoon sugar over the top of the batter. Bake until golden and a toothpick inserted comes out with dry crumbs, 15-18 minutes.
Cool in the pan for a few minutes, then turn out onto a wire rack to cool completely.
Muffins will keep in an airtight container at room temperature for up to 2 days.