In a blender or large bowl, combine sourdough discard and eggs. Whisk vigorously until fully combined and no streaks of egg yolk remain.
Add whole milk, water, melted and slightly cooled butter, salt, and if making sweet crepes, sugar and vanilla. Sift or sprinkle in the all-purpose flour and whisk until completely smooth and lump-free.
Pour batter into a bowl or jug, cover loosely, and let rest at room temperature for 20 to 30 minutes. For stronger sourdough flavor, refrigerate for up to 24 hours.
Set a 10-inch non-stick skillet over medium heat and preheat for 2 to 3 minutes. Add a small knob of butter and swirl to coat the pan evenly.
Lift the pan off the heat, pour approximately 1/4 cup of batter into the center, and immediately tilt and rotate the pan to spread the batter into a thin, even layer. Set the pan back on the burner.
Cook the crepe for 1 to 2 minutes until the edges look dry and pull away slightly from the pan. The surface should turn from glossy to matte.
Slide a wide, thin spatula underneath the crepe and flip it in one confident motion. Cook the second side for 30 to 45 seconds until lightly golden with a few spots.
Slide the finished crepe onto a plate. Stack each subsequent crepe directly on top of the last. Lightly re-butter the pan between each crepe.
Fill each crepe with sweet or savory fillings. Fold in half over the filling, then fold again into a quarter triangle, or roll tightly like a thin burrito. Serve immediately while warm.