In a medium mixing bowl, combine the flour, baking powder, salt, and sugar. Whisk to blend thoroughly.
In a small bowl, whisk the egg with 3/4 cup of the milk.
Add the egg and milk mixture to the dry ingredients along with the butter. Whisk until smooth. Add more milk in 1 tablespoon amounts until you have a fairly thick, but spreadable batter. You want the batter to spread on the griddle or skillet to about 1/4-inch thickness.
Heat a small amount of vegetable oil over medium heat. Use a 1/4-cup measuring cup to scoop the batter onto the pan.
Cook a pancake until bubbles appear over the top and the edges begin to look slightly dry.
Flip the pancake and continue to cook until the bottom is golden brown.