Add enough oil to a large pot to fill it about an inch deep. Set the burner to medium-high heat and heat the oil to 375 F/190 C.
While the oil is heating it is time to make the pastry. Add the water, salt, and butter (or oil if you are making authentic Spanish Churros), heat until the butter melts and the mixture begins to boil. Pour in all of the flour at once and mix quickly with a wooden spoon until the dough comes together. Keep mixing and stirring for about 30 seconds.
Now remove it from the heat and transfer the dough to a large bowl. Stir the dough continually until it cools down and is only warm to the touch. Stir in one egg, it will take a bit of time for it to incorporate, so be patient. Then proceed with the last egg. Or if you want to make more authentic or Vegan churros, leave the eggs out.
Add a large star tip to a piping bag and fill it up with the dough and twist the top. A little trick for filling piping bags is to put it in a large tall glass and fold the opening over the rim of the glass.
Pipe about a 5 to a 6-inch strand of dough gently into the hot oil. Use your finger or scissor to snip off the dough near the tip of the piping bag. Add 4 or 5 more strands of dough. Don't overcrowd the pot of oil. Cook the churros for 2 minutes or so turning them occasionally with tongs. Once golden brown, remove the homemade churros and place them on a wire rack or paper towel to drain/dry.
Mix together the cinnamon and the sugar in a pie plate or something like that, and then roll the churros in the cinnamon and sugar. You may also fill them with Nutella or something like that, using an injector tip and piping bag. Enjoy!