In a deep-fryer or heavy-bottomed pot, heat enough peanut oil to come halfway up the sides of the pot, to 375 degrees F.
Mix together the sugar and cinnamon in a small bowl and set aside.
Slice the seamless dough sheets into 1-inch strips from the shorter length of the dough. Make sure that the strips are not longer than your deep-fryer is wide. Twist each dough strip, and then drop, 3 at a time, into the fryer. Fry the donut sticks until golden brown and crisp, about 1 1/2 to 2 minutes, flipping with tongs about half way through. Remove the donuts from the fryer and dust with the cinnamon-sugar mixture. Serve with the chocolate sauce.
In a heavy saucepan over medium heat, combine the first 6 ingredients and bring to a simmer. Whisk in the chocolate, vanilla, and butter and stir until the sauce is smooth.