Preheat a griddle or large frying pan over medium heat to about 350°F and lightly grease with butter or vegetable oil.

In a medium mixing bowl, whisk together the milk, eggs, melted butter, and vanilla extract until smooth and slightly frothy.

In a separate bowl, whisk together the flour, sugar, baking powder, baking soda, and salt until well combined and airy.

Pour the wet ingredients into the well of the dry ingredients, and stir gently until just combined; it's okay if it's slightly lumpy.

Pour about ¼ cup of batter onto the heated griddle for each pancake. Cook until bubbles form on the surface, about 2 minutes, then flip and cook for another 1-2 minutes.

Transfer cooked pancakes to a serving plate or keep warm in a 175-200°F oven until the batch is done.