Set up a wire cooling rack over a baking sheet lined with paper towels. Bring eggs to room temperature and measure all ingredients. Mix cinnamon and sugar in a shallow dish and attach star tip to piping bag.
Combine water, butter, sugar, and salt in a medium saucepan. Bring to a full rolling boil over medium-high heat, stirring occasionally.
Remove from heat and add all flour at once, stirring vigorously with a wooden spoon until smooth and forming a ball. Return to low heat and cook 30 seconds, stirring constantly.
Transfer dough to a stand mixer and let cool 5-7 minutes until warm. Add vanilla, then beat in eggs one at a time until smooth and glossy.
Fill piping bag two-thirds full with warm dough, twisting the top to push dough toward the tip.
Heat 2 inches of vegetable oil in a heavy pot to 360-375°F (182-190°C). Use a candy thermometer to monitor temperature.
Pipe 4-6 inch lengths of dough directly into hot oil, cutting with scissors. Fry 3-4 at a time for 2-3 minutes per side until deep golden brown.
Remove with slotted spoon and immediately roll in cinnamon sugar mixture while hot. Transfer to wire rack.
Heat heavy cream in a small saucepan until simmering. Remove from heat, add chopped dark chocolate, let sit 2 minutes, then whisk until smooth. Add pinch of cinnamon and salt.