In a large bowl, whisk flour, sugar, baking powder, baking soda, and salt until evenly combined.
In another bowl, whisk together eggs, buttermilk, milk, melted butter, and vanilla extract.
Pour wet mixture into dry ingredients. Stir gently until just combined; a few lumps are fine. Avoid overmixing.
Heat a non-stick pan or griddle over medium heat and lightly grease with butter or oil.
Pour batter onto the skillet. Cook until bubbles form on the surface and edges are set, about 2–3 minutes. Flip and cook another 2 minutes until golden.
Stack pancakes, top with butter, maple syrup, fresh fruit, or your favorite toppings.