In a medium-sized mixing bowl, add the flour, sugar, baking powder, baking soda and salt and whisk to combine.
In a large measuring cup, combine the eggs, buttermilk, melted butter and vanilla extract and whisk to break up the eggs.
Add the wet ingredients to the dry ingredients and gently fold them together until well-combined and set aside. (Note: You don't want to overmix - the mixture should still be a little lumpy.)
Heat a pan or non-stick griddle over medium heat, then add about a tablespoon of butter to grease the pan.
For each pancakes, pour about ⅓ cup batter on the griddle and let it spread out into a 4" round pancake. Depending on the size of your pan, you may be able to cook up to 3 at a time.
Allow the pancakes to cook until bubbles appear on the surface and the edges are beginning to look cooked, or about 2 minutes. Flip the pancakes, using a spatula, and continue to cook the other side until golden and cooked through, or about 1 minute more.
Repeat this process with remaining batter. Serve pancakes with butter, syrup or your favorite toppings. Enjoy!