Fill a deep fryer or large saucepan with 2 quarts of vegetable oil. Heat the oil to 375°F.
In a large bowl, whisk together milk, egg, vanilla, and melted butter. Stir in 1 cup of pancake mix until the batter is smooth and free of lumps.
Dip each cream-filled chocolate sandwich cookie into the batter, letting the extra drip off. Carefully place the cookie into the hot oil. Fry in small batches for about 2 minutes, turning halfway, until golden brown.
Use a slotted spoon to remove the cookies and drain them on paper towels. Optionally, dust with powdered sugar before serving.