Using a blender or an immersion blender, combine milk, sourdough starter, eggs, melted butter, flour, salt, and optional vanilla and sugar.
Blend or whisk until completely smooth and no lumps remain. Let the batter rest for 15–30 minutes (or cover and refrigerate overnight for better texture and flavor).
Warm a nonstick skillet or crepe pan over medium high heat. Lightly butter (or oil) the bottom of the pan.
Pour about ¼ cup of the sourdough crepe batter into the pan, swirling to coat the bottom in a thin, even layer.
Cook for 1–2 minutes until the edges lift and the bottom is golden brown. Flip and cook another 30–60 seconds.
Transfer to a plate and repeat with remaining batter, re-buttering the pan as needed.