In a medium pot, combine water, butter, sugar, salt, and cinnamon; cook over medium heat until it comes to a rolling boil.
Add the flour all at once and reduce heat to medium low. Mix, using a wooden spoon/ spatula, until flour is fully incorporated. The dough should pull away from the pot to stick to itself. (Using a whisk may break it as the dough becomes thicker. )
Let cool for about 15 minutes (check that it's cool enough to the touch that it won't cook the eggs), then stir in the eggs. It will separate but keep mixing- trust the process and it will come back together as a dough.
Transfer the dough to a churrera or to a piping bag fitted with a wide, round, or open-starred tip.
In a medium bowl, combine the remaining 1 cup sugar and 1 teaspoon cinnamon.
Set a paper towel-lined plate next to the stove.
In a deep fryer, large pot, or high-sided skillet, heat the oil to 375°F.
Pipe 6-inch churros into the oil, frying a few at a time without overcrowding the pan.
Let fry, turning occasionally to cook evenly, until deep golden brown, 3 to 7 minutes total, depending on the thickness of the churro.
Remove the churros and transfer briefly to the prepared plate.
Quickly transfer the hot churros from the plate to the bowl of cinnamon-sugar mixture; toss to coat the churros.
Serve hot.
