Adjust the oven rack to the middle position and preheat oven to 425° (220° C).
Prepare your muffin tin by greasing or buttering the cups, with a little grease on the flat part of the muffin tin.
Whisk flour, baking powder, baking soda, and salt in a medium-sized bowl.
Whisk mashed bananas, 1/2 cup granulated sugar, eggs, butter, and vanilla in a large bowl until all the ingredients are well incorporated, and there are no banana chunks.
Add dry ingredients to the banana mixture and mix until fully incorporated, but don't overmix.
Gently fold in the blueberries.
Fill each muffin cavity to the top using a large spoon or 1/2 cup measuring cup.
Sprinkle muffins with coarse sugar.
Place in preheated oven and bake for 15-18 minutes, until a cake tester inserted in the center of a couple of muffins comes out clean.
Let the muffins cool in the muffin tin on a wire rack for at least 10 minutes before removing. Then let them cool for another 5-10 minutes before serving.
See Note 3 for tips on storing muffins.