In a medium bowl, whisk together the flour, sugar, baking powder, and salt. In another bowl, whisk together the eggs, milk, melted butter, and vanilla until smooth.
Pour the wet ingredients into the dry ingredients and stir gently until just combined — the batter should remain slightly lumpy.
Heat a large frying pan or skillet over medium heat and lightly grease with butter.
Using a ¼-cup ladle, pour small pools of batter spaced apart. When bubbles form on the surface and the edges start to dry (after about 2½ minutes), flip each pancake.
Cook for another 2 minutes until golden and fluffy. Transfer to a baking sheet and keep warm in the oven. Serve with maple syrup, praline, or berries.