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To make the crepe batter, whisk flour, sugar, and salt together in a large bowl. Set aside.
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In a medium bowl, whisk together milk, butter, eggs, and vanilla extract. Use an immersion blender to combine wet and dry ingredients until mixture is smooth (or transfer to a blender and blend until smooth, then pour back into bowl).
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Cover bowl with plastic wrap and refrigerate for 2-24 hours. Stir batter before cooking.
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Heat a 10-inch non-stick pan over medium-low heat and then add a bit of butter to coat the pan. Scoop ¼ cup of batter into the pan and swirl it around to completely cover the bottom. Cook until the edges are slightly browned, about one minute.
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Gently flip with a spatula and cook until underside is golden brown, about another 30 seconds-1 minute.
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Transfer crepe to a baking sheet lined with parchment paper. Repeat with the remaining batter and continue to stack the crepes on top of each other.