Heat a nonstick griddle or a skillet over medium-low heat to 375°F.
In a large mixing bowl, whisk together the flour, sugar, baking powder, baking soda, and salt
Heat the butter in a microwave or on the stove top until just melted. Let it cool for a few minutes before adding it to the wet ingredients.
In a separate medium bowl, whisk the eggs, then add the buttermilk, melted butter and vanilla extract. Whisk until the mixture is smooth and well combined.
Pour the buttermilk mixture into the large bowl of dry ingredients. Whisk together until the mixture is just combined. Some lumps are OK. Be careful not to overmix or the pancakes will be dense.
Allow the batter to rest for about 10-15 minutes. This gives the baking powder and baking soda time to activate, resulting in extra fluffy pancakes.
Lightly grease your cooking surface with vegetable oil. Pour a small amount of oil onto the griddle and gently wipe it with a paper towel.
Use a small measuring cup to pour one-third cup of batter onto the hot griddle or skillet. A one-third cup measuring cup will form pancakes about 6 inches in diameter. A one-fourth measuring cup will form pancakes 4-5 inches in diameter.
Cook until bubbles form on the surface of the pancakes, the edges begin to look dry and set, and the bottom is golden-brown, about 3 minutes. If the pancakes are browning too quickly, reduce the heat. Flip them with a spatula. Cook for an additional 1-2 minutes, or until golden brown on both sides.
Transfer the pancakes to a plate and serve them hot with warmed maple syrup and your favorite pancake toppings.