Put the pancake mix in a bowl. In another bowl, whisk the milk, 2 tablespoons of oil, the egg and egg yolk, and vanilla. Pour this mixture over the pancake mix and stir to combine well. Put the batter in a measuring cup with a spout or similar vessel, such as a small pitcher.
Line a plate with paper towels. Pour oil into a cast-iron skillet to a depth of about 1/2-inch. Heat the oil over medium heat to a temperature of 325ºF to 350ºF.
Hold a funnel over the oil, a couple of inches from the surface.