Sift flour, baking powder, and sugar together in a bowl; pour in milk and butter and mix well. Stir eggs and vanilla extract into flour mixture until batter is smooth.
Heat a lightly oiled griddle over medium heat. Drop batter by large spoonfuls onto the griddle and cook until bubbles form and the edges are dry, 3 to 4 minutes. Flip and cook until browned on the other side, 2 to 3 minutes. Repeat with remaining batter.