Add milk, flour, sugar, salt, butter, vanilla and eggs to a blender, then blend on low speed until well combined, about 10 seconds.
Scrape sides and bottom of blender if there's any flour sticking and blend a few seconds longer.
Lightly butter skillet then lift pan and pour a scant 1/4 cup batter into pan, immediately tilt and swirl pan in circular motion to evenly coat entire bottom portion of pan with batter.
Cook until golden brown brown on bottom then use an offset spatula to lift an edge of the crepe, grab the edge of the crepe with your fingertips and flip crepe to opposite side. Cook until golden brown spots appear on bottom.
Transfer to a wire rack. Repeat until all of the batter has been used up (if needed reduce burner temperature slightly).