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In a blender, mix the milk and egg until frothy.
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Add the flour, sugar, salt, and vanilla and blend until everything is well incorporated (around 1 minute).
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Let the batter rest in the refrigerator for around 30 minutes (you can also do it overnight but 30 minutes is enough).
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Preheat a big pan over medium heat and grease with some butter.
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Pour around 1/4 cup of the batter and swirl to completely cover the pan.
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Cook for 2 minutes and with the help of a spatula and your hands flip the crepe. Cook for an additional 30 seconds.
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Repeat the process with the rest of the batter.