In a medium bowl, whisk flour, granulated sugar, baking powder, and salt.
In a large bowl, whisk milk, egg, and vanilla. While whisking, stream in melted butter and whisk to combine.
Gently fold dry ingredients into milk mixture until just combined (do not overmix; some lumps are okay).
Preheat a griddle or other large heavy skillet over medium heat until hot but not scorching, 2 to 3 minutes.
Melt enough butter to cover surface of griddle, then pour about ¼ cup batter onto griddle.
Cook pancake until bubbles form on top and sides start to lift from pan, 2 to 3 minutes.
Flip and cook until bottom is golden brown and pancake is fluffy, 2 to 3 minutes.
Transfer to a wire rack. Wipe off griddle, then repeat with more butter and remaining batter (you should get about 10 pancakes).
Divide pancakes among plates. Serve with butter and syrup.
