Preheat the oven to 400°F and line a 12-cup standard muffin pan with paper liners.
In a small saucepan, melt the butter over medium heat. Once melted, keep on heat, it will start to foam and crackle. Swirl the pan occasionally.
Cook until the butter starts to turn brown (brown bits will form first in the bottom) and smells nutty. Keep an eye on it and swirl occasionally so it does not burn. Remove from the heat and set aside to cool.
In a large bowl, whisk together the flour, brown sugar, baking powder and salt.
In a small bowl, whisk together the cooled browned butter, buttermilk, egg and vanilla.
Add wet ingredients to dry ingredients and mix with a spatula until just combined. Do not overmix. A few streaks of flour in the batter is ok and will be incorporated later when you mix in the blueberries.
Put the fresh or frozen unthawed blueberries in a small bowl and sprinkle 1 tablespoon of flour over them to coat the blueberries to prevent them from sinking to the bottom of the batter. Gently fold the flour-coated blueberries into the batter.
Evenly divide the batter among the 12 muffin tin cups.