Pour milk into a microwave-safe bowl. Heat in the microwave until slightly warm, 20 to 30 seconds. Whisk in butter. Whisk in eggs. Add flour, baking powder, vanilla extract, and salt; blend briefly with an immersion blender to make a smooth batter.
Heat a lightly oiled griddle over medium-high heat. Drop batter by large spoonfuls onto the griddle and cook until bottom is golden brown, 2 to 3 minutes. Flip and cook until browned on the other side, 2 to 3 minutes. Repeat with remaining batter.