The churros. In a small saucepan, heat the water, salt, sugar, and butter. Meanwhile, in a bowl, sift the flour. When water reaches a rolling boil, add the sifted flour and stir continually until you get a dough and it unsticks from the sides. Remove from heat and transfer the dough to a bowl. Let it cool for few minutes (but only for few, it should still be warm).
Beat the eggs and add to the dough while stirring. Now transfer the dough into a piping bag with a star nozzle.
Heat the oil in a deep frying pan until it reaches 360°F (180°C). Squeeze strips of dough into the oil and fry, turning once, until golden brown. Do not overcrowd the pan. When done, drain on paper towels. Mix sugar and cinnamon together and roll your churros in this mixture.
The hot chocolate. Dissolve the cornstarch in 1 cup of the milk. Set aside. Place the remaining cup of the milk in a saucepan together with the chocolate. Cook on a low heat, stirring continuously, until the chocolate has melted. Add the cornstarch and milk mixture and whisk well. Add the sugar. Cook for 5 minutes more, whisking, until the mixture has thickened. If it's not smooth, whisk a little bit more.
Pour the hot chocolate into a cup or a bowl and dip your churros into it. Enjoy!