In a large mixing bowl, whisk together the flour, sugar, baking powder, baking soda, and salt until well combined.
In another bowl, beat the eggs and then add the buttermilk, melted butter, and vanilla extract. Mix until smooth.
Pour the wet ingredients into the dry ingredients and stir gently until just combined. Be careful not to overmix; a few lumps are okay.
Preheat a non-stick skillet or griddle over medium heat. Lightly grease with butter or cooking spray.
Pour 1/4 cup of batter onto the skillet for each pancake. Cook until bubbles form on the surface and the edges look set, about 2-3 minutes.
Flip the pancakes and cook for another 1-2 minutes until golden brown.
Repeat with the remaining batter, adjusting the heat as necessary to prevent burning.
Serve warm with your favorite toppings such as maple syrup, fresh fruit, or whipped cream.