Pour the vegetable oil into a large pot, ensuring it's at least 2 inches deep. Heat until it reaches 350°F.

In a bowl, whisk together the beaten egg, vanilla extract, and milk. Add the Bisquick mix and whisk until smooth.

Place an Oreo on a spoon, submerge it in the batter, and ensure it's fully coated. Scoop some batter with it.

Carefully lower the spoon with the coated Oreo into the hot oil and fry for 30 to 60 seconds until golden brown.

Remove the fried Oreo with a slotted spoon and place it on paper towels. Dust with confectioners' sugar before serving.