Combine milk, egg, salt, sugar, butter, flour, and yeast in a bread machine.

Start the dough cycle.

Remove the dough from the bread machine to a lightly floured surface.

Cover with a large mixing bowl and let rest for 10-15 minutes.

Divide the dough into 10 balls.

Flatten and gently stretch each ball into an 8x6-inch oval (beaver tail shape).

Heat vegetable oil in a deep-fryer or large saucepan to 350 degrees F (175 degrees C).

Cook the dough one or two at a time in the hot oil until lightly browned on each side, about 2 minutes per side.

Drain on a paper towel-lined plate.

Sprinkle with cinnamon sugar to serve.