To make the churro dough: Combine 1 cup of water with the butter or margarine and the salt in a saucepan and bring to a boil over high heat. Using a wooden spoon, stir in flour. Reduce the heat to low and stir vigorously until the mixture forms a ball, about 1 minute. Remove the dough from the heat and, while stirring constantly, gradually beat the eggs into the dough.

To make the chocolate for dunking: In a small bowl, dissolve the cornstarch in 1 cup of milk and reserve. Combine the chocolate with the remaining cup of milk in a saucepan. Stirring constantly, melt the chocolate over medium-low heat. Whisk the sugar and the dissolved cornstarch into the melted chocolate mixture. Reduce the heat to low and cook, whisking constantly, until the chocolate is thickened, about 5 minutes. (Add extra cornstarch if it doesn't start to thicken after 5 minutes.) Remove the pan from the heat and whisk until smooth then reserve in a warm place.

Heat about 2 inches of oil in a heavy, high-sided pot over medium-high heat until the oil reaches 360 degrees F. Mix the sugar with the cinnamon on a plate and reserve.

Meanwhile, spoon the churro dough into a pastry bag fitted with a large tip. Squeeze a 4- inch strip of dough into the hot oil. Repeat, frying 3 or 4 strips at a time. Fry the churros, turning them once, until golden brown, about 2 minutes per side. Transfer the cooked churros to a plate lined with paper towels to drain.

When the churros are just cool enough to handle, roll them in the cinnamon-sugar (in Spain churros are simply rolled in sugar.)

Pour the chocolate into individual bowls or cups. Serve the warm churros with the chocolate dip.