In a medium bowl, beat the egg. Add in the vanilla yogurt and mix well. Mix in the baking soda. The batter will form bubbles when the baking soda reacts with the yogurt. Mix in the flour. Mix in the oil. Let batter stand for 5 minutes.
Heat a non-stick skillet or griddle over medium heat. Coat the pan in a very thin layer of oil.
Drop the pancake batter by ¼ cups.
When the pancakes start to bubble around the edges (about 2 minutes), flip and cook for about 2 more minutes.