Start by adding the flour, sugar, baking powder, and salt to a large mixing bowl. Whisk everything together well so the dry ingredients are evenly distributed before adding any liquid.
In a separate bowl, combine the milk, egg, melted butter, and vanilla extract. Whisk until the mixture is smooth and fully blended.
Pour the wet ingredients into the bowl with the dry ingredients. Stir gently with a spoon or whisk just until the batter comes together. Do not keep mixing once the flour is incorporated.
Let the batter rest for a minute or two while you heat your skillet or griddle over medium heat. Lightly grease the surface with butter or oil so the pancakes cook evenly and release easily.
Scoop about 1/4 cup of batter onto the hot skillet for each pancake. Leave a little space between them so they are easy to flip once the tops start to bubble.
Cook the pancakes until bubbles form across the surface and the edges start to look set. Carefully flip them and continue cooking until the second side is golden brown and the center is cooked through.
Remove the pancakes from the skillet and repeat with the remaining batter. Add a little more grease to the pan as needed between batches.
Serve the pancakes warm with butter, syrup, fresh fruit, whipped cream, or any toppings you like. They are best served fresh, but leftovers reheat well for an easy breakfast later.