In a large bowl, whisk together the flour, baking powder, salt, and sugar.
In another bowl, beat the egg, then mix in the milk, melted butter, and vanilla extract.
Pour the wet ingredients into the dry ingredients and stir gently until just combined. A few lumps are okay - overmixing can make pancakes dense.
Let the batter rest for 5 minutes while you heat a non-stick skillet or griddle over medium heat.
Lightly grease the skillet with butter or oil. Pour about ¼ cup of batter per pancake into the skillet.
Cook until bubbles form on the surface and the edges start to look set, about 2–3 minutes. Flip and cook for another 2 minutes until golden brown.
Repeat with the remaining batter, keeping the cooked pancakes warm in a low oven if needed.