Put water, butter, sugar, salt, and vanilla in a pot and bring to a boil until it bubbles.
Reduce the heat and add flour, stirring quickly until the dough comes together and releases from the pot.
Stir for a few minutes to "toast" the dough (it should not change color).
Let the dough cool slightly before adding eggs one at a time while whisking.
Whisk until the dough is smooth and elastic.
Put the dough into a cloth piping bag or two disposable bags with a star nozzle.
Heat the oil to 175 degrees Celsius (347 degrees Fahrenheit) and pipe lengths of dough into the hot oil.
Cut with scissors at the desired length.
Fry for a few minutes until they are beautiful and golden.
Place them on absorbent paper and sprinkle with cinnamon sugar.
Put water and sugar in a pot and bring to a boil.
Boil away the water and let the syrup cook into a caramel until it turns golden.
Gradually reduce the heat so it doesn't burn.
When the caramel is golden, turn the heat completely down.
Add butter and stir well.
Heat again and add cream in a thin stream while continuously whisking.
Bring the caramel to a boil and season with sea salt.
Serve the caramel sauce with the warm churros.
Enjoy!
