Mix the sugar and cinnamon in a wide dish and set it beside the stove.
Bring the water, butter and salt to a full boil in a saucepan, so the butter is completely melted.
Tip in all the flour at once and stir hard with a wooden spoon. It will look lumpy, then come together into a smooth ball that pulls away from the sides. Keep stirring over the heat for 1 minute more to cook the flour.
Take the pan off the heat and spread the dough up the sides to cool it for 5 minutes. It should be warm, not hot, or the eggs will scramble.
Beat in the eggs one at a time, working each one in completely. The dough will look slippery and split at first, then come back together into a thick, glossy paste.
Spoon it into a piping bag fitted with a large closed star tip. The ridges are not decoration, they are what lets steam escape.
Heat the oil to 350F to 360F in a deep, narrow pan, about an inch deep and no more than a third full.
Pipe 5 inch lengths directly over the oil, cutting them off with scissors, 3 or 4 at a time. Fry 2 to 3 minutes, turn with tongs, and fry 2 minutes more, until deep golden and firm all round.
Lift onto a rack for 30 seconds, then roll each one in the cinnamon sugar while it is still hot and slightly oily, which is what makes the coating stick.