Whisk eggs until smooth. Add sugar (if using), melted butter, salt, and vanilla extract. Mix well.
Gradually whisk in the milk, then stir in the sourdough starter. Slowly add flour and mix until smooth.
Cover and refrigerate for at least 1 hour or overnight.
Heat a pan over medium heat and lightly grease it with butter. Pour a ladleful of batter into the pan, tilting it to coat the surface evenly. Cook until the edges lift and the bottom is golden, then flip and cook the other side. Repeat with the remaining batter.
Serve warm with your choice of toppings.