Whisk flour, sugar, baking powder, and salt in a large bowl.
Whisk eggs, milk, melted butter, and vanilla in another bowl.
Pour the wet ingredients into the dry ingredients.
Stir gently until combined, leaving small lumps.
Rest the batter for 5 to 10 minutes.
Heat a skillet or griddle over medium heat.
Grease the pan lightly with butter or oil.
Pour 1/4 cup batter for each pancake.
Cook until bubbles appear and edges look set.
Flip once, then cook until golden underneath.
Move cooked pancakes to a plate or warm oven.
Repeat with the remaining batter.
Keep cooked pancakes warm in a 200-degree oven.