In a large mixing bowl, whisk together the all-purpose flour, baking powder, salt, and white sugar.
In a separate bowl, whisk the egg and then add the milk, melted butter, and vanilla extract. Mix until well combined.
Pour the wet ingredients into the dry ingredients. Stir gently until just combined. It's okay if there are a few lumps; overmixing can make pancakes tough.
Preheat a griddle or non-stick skillet over medium-high heat. You'll know it's ready when a drop of water sizzles on the surface.
Lightly grease the griddle or skillet with a small amount of butter or cooking spray.
For each pancake, ladle approximately 1/4 cup of batter onto the griddle. Use the back of a spoon to spread it into a circular shape if needed.
Watch for bubbles to form on the surface of the pancakes. This usually takes about 2-3 minutes.
Once the bubbles have formed and the edges appear set, flip the pancakes using a spatula. Cook the other side for an additional 2-3 minutes or until golden brown.
Transfer the cooked pancakes to a plate and keep them warm. You can serve them immediately with your favorite toppings.