Whisk together flour, sugar, baking powder, baking soda, and salt in a large bowl.
In a medium bowl, melt the butter and warm the milk in the microwave.
Whisk in the egg and vanilla extract until smooth.
Add the wet ingredients to the dry ingredients and whisk until mostly smooth. Don't overmix, a few lumps are okay.
Heat a large skillet, griddle, or nonstick pan over medium heat. Let the pan get hot for 2 minutes and then lower the heat to medium-low heat. Grease the pan with some butter.
Pour ¼ cupfuls of batter onto the pan. Work in batches and don't overcrowd the pan. Cook until the surface is covered with bubbles and the sides are starting to look golden brown. Use a large spatula to flip the pancakes and continue to cook for another 1-2 minutes on the other side.
Transfer to a plate and continue to cook in batches until all the batter has been used.
Serve the pancakes warm with butter and syrup.