Special equipment: a deep-fry thermometer; a pastry bag or resealable bag fitted with a 1/2-inch star tip
Fill a large, wide pot with about 1 1/2 inches of oil. Heat over medium-high heat until the oil reaches 365 degrees F on a deep-fry thermometer.
Meanwhile, whisk together the pancake mix, allspice and 1/2 teaspoon of the cinnamon in a large bowl. Add the hot water and whisk until well combined. Spoon the dough into a pastry bag or resealable plastic bag fitted with a 1/2-inch star tip.
Combine the sugar and the remaining 1 1/2 teaspoons cinnamon in a small bowl, then transfer to a sugar shaker (or use a small mesh strainer).
When the oil has reached temperature, carefully pipe approximately 3-inch tubes of batter directly into the oil, working in batches if necessary and using a knife to cut the dough between churros. Fry, turning occasionally, until golden brown all over, about 3 minutes per batch. Drain the churros very briefly on a paper-towel-lined plate, then sprinkle with the cinnamon sugar.
Serve immediately with chocolate sauce on the side for dipping if using.