In a large mixing bowl, combine the flour, sugar, eggs, and half of the milk. Whisk with a balloon whisk until the batter is completely smooth and lump-free. Add the remaining milk and the melted butter. Continue whisking until the mixture forms a silky, cohesive batter.

Pour the batter through a fine-mesh sieve into a large measuring jug or bowl to ensure absolute smoothness. Alternatively, blend all the ingredients together in a food processor or a blender, which will eliminate the need for straining.

Heat a 9.5-inch/24-centimeter nonstick skillet or a dedicated crepe pan over low to medium heat. Lightly brush the surface with melted butter using a pastry brush. Pour about ⅓ cup of batter into the center of the hot pan. Immediately lift and tilt the pan in a circular motion to spread the batter into a thin, even layer. You can also use the back of a ladle to help distribute the batter if needed. Cook for about 1 minute, or until the underside is lightly golden. Flip carefully with a thin spatula and cook the other side for another 30 seconds to 1 minute.

Transfer each crepe to a plate, stacking them directly on top of one another to prevent drying.