Heat 3 inches of oil in a large, deep skillet until a deep-fry thermometer registers 340 degrees. Combine the muffin mix, flour, sugar, baking powder and 1 teaspoon cinnamon in a bowl. Stir in the eggs, orange zest and buttermilk and whisk until combined.
Transfer half the batter to a pastry bag fitted with a large star tip (No. 844) and pipe 4-inch-long churros into the oil, about 4 at a time. (If you don't have a pastry bag, you can spoon the batter into the oil in lines.) Fry until golden, about 15 seconds per side, turning once. Remove with a slotted spoon to drain on paper towels. Repeat with the remaining batter.
Combine the remaining 1 teaspoon cinnamon with sugar to taste and sprinkle over the churros. Serve warm with the chocolate sauce.