Heat vegetable oil in a griddle or shallow frying pan over medium heat.
Whisk flour, sugar, baking powder, baking soda, and salt together in a bowl; stir eggnog into flour mixture until batter is smooth.
Pour enough batter into the heated griddle to make a 4- to 5-inch circle. Cook until bubbles appear around the edges and bottom is browned, about 5 minutes. Flip and cook until other side is evenly browned, about 5 more minutes. Repeat with remaining batter.