In a medium saucepan over medium heat, combine the water, butter, salt, and 1 tablespoon sugar and bring to a boil.
Add the flour to the pan all at once and cook, stirring vigorously, until stiff but smooth, about 4 minutes. (Enjoy the biceps workout while you’re at it!) Transfer the dough to a bowl and let it cool for about 5 minutes.
Whisk in the egg until the dough is very smooth.
Fill the prepared piping bag or resealable plastic bag with the dough. The 1/4-inch [6-mm] star-shaped tip may look too small, but trust us, the dough will swell when it fries and the star-shape will leave nice ridges on your churros. (You can refrigerate the dough in the piping bag overnight if you like. Bring the chilled dough to room temperature before using so it will squeeze more easily.)
Mix the cinnamon and 3 tablespoons sugar on a large plate.
In a large, heavy saucepan, pour enough oil to reach a depth of at least 2 inches (5 cm). Place the saucepan over medium-high heat until the oil reaches 350°F (180°C) on an instant-read thermometer. The oil is ready when a small drop of dough sizzles and falls to the bottom of the saucepan only to immediately rise to the top again.
Working carefully, hold the piping bag over the hot oil, squeeze out a few 6-inch (15-cm) lengths of churros dough, cut it off with clean scissors, and fry, turning once, until golden brown, 3 to 4 minutes. Don’t overcook or the churros will lose the creamy interior that makes them so irresistible. (This particular churros recipe is designed to have more crunch and less cake-like interior.) Fry the churros in batches, being careful not to overcrowd the pan.
Use tongs to move the fried churros to paper towels or a brown paper bag to drain briefly. Toss the warm churros in the cinnamon sugar while still hot and turn to completely coat them.
Serve immediately, with warm caramel sauce or hot chocolate for dipping, if desired.