To a large bowl, add the flour, milk, eggs, sugar, salt, butter and vanilla.
Whisk until the mixture is silky smooth and get frothy on the top.
Grease an 8-inch skillet with butter over medium-low heat.
Once the butter is melted, add about 1/4 cup of batter to the center of the pan. Tilt the pan so that the batter fills the entire bottom of the pan.
Cook for about 1 minute, then gently flip the crepe using a spatula.
Cook for one minute more or until golden.
Transfer to the plate, and repeat making additional crepes with the remaining batter. Stack the crepes on the plate, adding a layer of parchment between each to prevent sticking.
To serve, place one French pancake on a plate. Add fillings such as sliced banana, Nutella, or berries to the middle. Fold up the edges to make a semi-circle and fold once more. Repeat to make 2-3 pancakes per person.