In a large saucepan, bring water, butter, salt, and sugar to a rolling boil over medium-high heat. Once boiling, remove the pan from heat.
Stir in all the flour at once vigorously until fully incorporated, about 30 to 60 seconds. Return the mixture to heat and cook, stirring, for an additional 30 seconds. Transfer the mixture to a mixer with a paddle attachment or use a hand mixer.
Mix at medium speed, adding 3 eggs, one at a time, and vanilla while the mixer is running. Pause to scrape down the sides after each addition. Continue mixing until the dough is smooth, glossy, and all the eggs are fully incorporated. The dough should be thick but smoothly fall from the beaters when lifted. If it clings to the beaters, add the remaining 1 egg and mix until fully incorporated.
Heat oil to 370°F.
Using a pastry bag fitted with an 869 or large closed star tip, pipe 6-inch pieces, frying about three at a time. Fry each side for 90 seconds to 2 minutes or until golden brown.
Remove with tongs, let drain on a paper towel for about thirty seconds, then coat with cinnamon sugar.
Combine the chocolate and heavy cream in a bowl over a pot of barely simmering water. Stir occasionally until fully melted and well combined.