Turn on oven to the lowest temperature setting (generally about 150 degrees F), and place a large serving platter inside to keep warm.
In a large bowl, whisk together flour, sugar, baking powder, baking soda, and salt.
In another bowl, mix buttermilk, eggs, butter, and vanilla to blend.
Pour buttermilk mixture over the flour mixture, whisking until batter is smooth. (It should be thick, but fluid.)
Brush griddle with vegetable oil.
When hot, ladle approximately 1/4 C batter onto the griddle and cook until most of the bubbles that form on the surface pop and remain open, approximately 3 minutes. (The surface of the pancake should also get duller, and the underside of the pancake should be golden-brown.)
Flip the pancake with a spatula, and cook for 1 minute longer.
Remove the pancake to the platter in the oven to keep warm, and repeat with remaining batter.