Special equipment: a piping bag fitted with a large star tip
Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper.
Combine the water, butter, 2 tablespoons of the sugar, cardamom, salt and orange zest in a medium saucepan over medium heat. Bring to a simmer and cook until the butter melts, 2 minutes. Add the flour and whisk until the lumps are gone and the dough forms a ball. Turn the heat to low and cook, stirring with a wooden spoon, for 1 minute.
Whisk the vanilla and eggs in a small bowl until combined. Stir the egg mixture into the flour mixture in 3 additions, making sure each addition is fully incorporated before adding the next.
Transfer the dough to a piping bag fitted with a large star tip. Pipe 3-inch-long churros onto the prepared baking sheet, spaced 2 inches apart (see Cook's Note). Bake until golden brown, 22 to 25 minutes. Turn off the oven and leave the churros for another 10 minutes.
Combine the cinnamon and remaining 2 tablespoons sugar in a large plastic bag and shake to mix. Add the still-warm churros to the bag and shake gently to coat. Remove the churros and shake off any excess sugar. Best if served warm.
Make sure to pipe the churros nice and thick. Do this by putting pressure on the bag and piping slowly.