Whisk together flour, baking soda, salt, egg, and buttermilk until smooth.
Heat a griddle or a large heavy skillet over moderate heat until hot enough to make drops of water scatter over its surface, then brush with oil. Working in batches and using a 1/4-cup measure filled halfway, pour batter onto griddle and cook, turning over once, until golden, about 2 minutes per batch. Transfer to a heatproof plate and keep warm, covered, in oven.
Batter keeps, chilled and covered, 3 days. Thin as necessary with additional buttermilk or water, 1 tablespoon at a time, before using.