Add vanilla, butter and milk. Mix until incorporated well.
Blend eggs in, careful not to overheat. It's okay to have lumps.
Heat pan to medium. Pour mixture onto pan. Once it heavily bubbles, flip until slightly brown.
Notes
Be sure to soften the butter before adding it to the pancake butter. If the butter is cold, it won't combine well with the other ingredients and can cause the pancakes to spread to much during cooking.
Do not over mix your batter. You don't need a super smooth batter to make pancakes. Stop stirring once the ingredients are just combined.
You can make your pancake batter the night before and keep it covered in the fridge for a quick and easy breakfast in the morning.