Mexican Crullers (Churros)

To make the crullers: In a medium saucepan, heat 1 cup water, the butter, sugar, vanilla, and salt over medium-high heat until the edges of the liquid start to bubble. Add the flour all at once and stir briskly with a wooden spoon until well mixed and no lumps of flour remain. Remove from the heat. Add 4 of the eggs, 1 at a time, beating well with a wooden spoon after each. The dough should look soft and glossy and keep a "hook" shape when the spoon is pulled from the dough. If not, beat in the last egg. Scrape the dough into a pastry bag fitted with a star tip. Pour enough canola oil into a deep heavy skillet (cast iron is ideal) to fill 1-inch. Heat over medium heat until the tip of the handle of a wooden spoon gives off a slow steady stream of tiny bubbles. Carefully pipe the dough into the oil, forming 6-inch crullers. Pipe only as many crullers into the oil as fit comfortably. Overcrowding the pan will result in soggy crullers. Fry, turning once, until golden brown on each side. Drain on paper towels. Repeat with the remaining dough. Put the sugar and the cinnamon in a paper bag. Crimp the top and shake well to mix. Drop a few crullers at a time into the bag and shake until coated. Best served as soon as possible.