Melt your butter first and set it aside so that it has time to cool.
Meanwhile, combine the flour, sugar, baking powder, baking soda, and salt in a large bowl and whisk together until well-combined.
In a separate, medium-sized bowl, whisk together buttermilk, eggs, and vanilla extract.
Take your melted (slightly cooled) butter and slowly drizzle it into your wet ingredients while whisking, stirring until well-combined (the butter may separate and curdle if your other ingredients are cold and the butter is still hot).
Pour the wet ingredients into your dry ingredients and use a wooden spoon to stir until dry ingredients are about halfway incorporated into the batter. Now add your blueberries and gently fold them in while continuing to stir your batter. Take care that you do not over-stir your pancake batter or your pancakes will come out flat. Use a gentle hand when stirring, a few flour streaks in the batter are fine.
Allow your blueberry pancake batter to rest for 5 minutes before continuing.
Once batter has rested, spray a non-stick skillet with cooking spray or lightly brush with canola oil and place on burner on medium-low heat.
Allow the skillet to preheat before adding batter (this could take about another 5 minutes, and it's good to let your batter rest for this additional time, it will help give you thicker fluffier pancakes). Once skillet is heated (I usually test this by hovering my hand several inches above the pan and making sure I can feel the heat radiating from it) scoop pancake batter into pan (I use about ½-⅔ cup of batter per pancake).
Allow pancake to cook until edges begin to appear cooked and bubbles in batter begin to burst. Using a pancake spatula, carefully flip pancake and continue to cook several more minutes until pancake is golden brown.
Repeat until all batter is used -- I recommend spraying or brushing the pan between each batch of pancakes.
Serve warm.