In a large liquid measuring cup or batter bowl with a spout, whisk together milk, egg, and vanilla.
In a separate bowl, whisk together dry ingredients, except powdered sugar.
Add the dry ingredients to the wet, and whisk until completely smooth. Set aside.
In a medium, deep-sided pan or pot, heat 1" of oil to 375°F over medium-high heat. When you put the end of a wooden spoon in the pot and bubbles form around the spoon, it's ready. Reduce heat to medium.
Drizzle batter from cup in a thin line, swirling around the pan and overlapping as desired. Cook for 2 minutes or until light golden brown, then flip and cook another 2 minutes or until golden brown.
Dust with 2 tablespoons powdered sugar and serve. Repeat one more time with the remaining batter.