Whisk the milk, eggs, melted butter and vanilla in a large bowl until combined. Add the flour, sugar and salt; whisk until the batter is smooth, with no lumps.
Heat a medium nonstick skillet over medium heat; lightly brush with butter. Add 1/4 cup batter; swirl the skillet to coat the bottom with a thin layer of the batter. Cook until set on top and lightly browned around the edge, about 1 1/2 minutes. Gently lift and flip the pancake with a rubber spatula; cook until just browned on the other side, about 15 more seconds. Transfer to a plate and repeat with the remaining batter (do not brush the skillet with more butter). Fold into quarters and serve with butter and syrup or jam.