In a large bowl whisk together the all-purpose flour, baking powder, granulated sugar, and salt until evenly combined.
In a separate bowl whisk the large egg until blended. Add the warm whole milk, the melted unsalted butter, and the vanilla extract; whisk until the wet ingredients are combined.
Pour the wet mixture into the dry ingredients. Whisk gently until the batter is just combined and no large dry streaks remain—small lumps are fine. Do not overmix.
Heat a skillet or griddle over medium heat until hot. Lightly brush the cooking surface with some of the melted unsalted butter.
Use a 1/4-cup measuring cup to pour portions of batter onto the skillet, leaving space between pancakes. If needed, use the back of the cup to nudge each portion into a round shape.
Cook until bubbles appear on the surface and the edges look set and slightly dry and the bottom is golden brown (about 3 minutes). Flip and cook the second side until golden brown and cooked through (about 2–3 minutes).
Transfer pancakes to a plate and serve warm.