In a large bowl, combine egg, butter, milk, and baking mix. Whisk together until smooth. Pour into piping bag with a star tip. In a small bowl, stir together sugar and cinnamon.
Pour oil into a 10-inch heavy skillet to a depth of 1-inch. Heat oil to 350 degrees F. When oil is hot enough, pipe dough in lines, a few at a time, and fry about 30 seconds on each side, or just until deep golden. Drain on towels. While still hot, sprinkle with sugar and cinnamon mixture. Serve warm.
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