Preheat the oven to 375F (190C or 180C fan forced). Line a 12-cavity muffin pan with muffin papers. You'll end up with about 12-14 muffins in total.
In a very large bowl, whisk together the 2 cups flour, baking powder, baking soda and salt.
In a separate bowl, whisk together the melted butter, brown sugar, granulated sugar, eggs and vanilla extract.
Whisk the sour cream and mashed bananas into the butter mixture.
Make a well in the middle of the flour mixture. Then pour the wet ingredients into the dry ingredients. Gently fold the ingredients together using a rubber spatula or wooden spoon until they look about 90% combined. There will still be lumps.
If using frozen berries, toss the berries with the 2 teaspoons of flour. Then gently fold the berries into the batter using a rubber spatula or wooden spoon. If the batter still has lumps, that is OK - they're likely just pieces of banana.
Spoon the batter into the prepared muffin pan, filling each muffin paper to the top. You should end up with 12-14 muffins in total.
Bake in the preheated oven for about 18-22 minutes, or until an inserted toothpick comes out clean or with blueberry juice but no muffin batter.
Cool the muffins in the pan for at least 10 minutes, then transfer to a wire rack to continue cooling.