In a large bowl, whisk together the flour, sugar, baking powder, baking soda, and salt.
In a separate bowl, whisk together the eggs, buttermilk, melted butter, and vanilla extract.
Pour the wet ingredients into the dry ingredients. Stir gently until just combined, leaving a few small lumps in the batter.
Let the batter rest for 5–10 minutes while heating a nonstick skillet or griddle over medium-low to medium heat.
Lightly grease the cooking surface with butter or neutral oil.
Pour approximately ¼ cup of batter onto the skillet for each pancake.
Cook for 2–3 minutes, until bubbles appear across the surface and the edges begin to look set.
Flip carefully and cook for another 1–2 minutes, until the second side is golden and the pancake is cooked through.
Repeat with the remaining batter, adjusting the heat as needed and lightly greasing the skillet between batches.
Serve warm with butter, maple syrup, and your favorite toppings.