In a small bowl, whisk together eggs and vanilla. Set aside.
In a separate small bowl, stir together flour, sugar, baking soda, and salt.
In a medium bowl, stir together the sour cream with the dry ingredients until just barely combined (don't overmix.) Whisk in the egg mixture until just combined.
Heat a griddle over medium-low heat and melt some butter in the pan. Drop batter by 1/4 cup servings onto the griddle. Cook on the first side until bubbles start to form on the surface and edges are starting to brown. Flip to the other side and cook for another minute. (Pancakes will be a little on the soft side.)