Heat a nonstick skillet or griddle over medium heat. Lightly grease with butter or oil.
In a large bowl, whisk together the flour, sugar, baking powder, baking soda, and salt.
In another bowl or large measuring cup, whisk the buttermilk, eggs, melted butter, and vanilla until well combined.
Pour the wet ingredients into the dry ingredients. Stir gently with a spatula until just combined. Do not overmix—lumps are okay. Let the batter rest for 5 minutes.
Scoop ¼ cup of batter onto the hot skillet for each pancake. Cook until bubbles form on the surface and the edges look set, about 2–3 minutes. Flip and cook the other side for 1–2 minutes until golden brown.
Transfer to a plate and keep warm while cooking the rest. Serve immediately with your favorite toppings.