Combine the flour and salt in a small saucepan. Stir in the boiling water with a wooden spoon to make a thick batter, then cook over medium heat for 1 minute. Switch off the heat and add the baking powder, folding over the dough to mix it through. Allow to cool for 10 minutes, then stir in the aquafaba until smooth. The dough will be quite stiff.
Fit a heavy-duty piping (icing) bag with a star nozzle at least 1 cm (½ in) thick and place it in a tall jug, furling the edges over the rim to hold it in place. Spoon the churro dough into the bag, but don’t overfill it, so you can twist the bag tightly shut. Leave to rest while you prepare the oil.
Heat 5–7.5 cm (2–3 in) of neutral-flavoured oil in a large heavy-based saucepan until the temperature registers above 175°C (345°F) on a kitchen thermometer, or when the handle of a wooden spoon instantly bubbles when placed in the oil. Adjust the temperature slightly to keep it around 175°C (345°F) while frying the churros.
You can pipe the churros straight into the hot oil and use scissors to snip off your ideal lengths as you go. For beginners and those who seek control of the whole process, pipe each churro onto baking paper, so you can just drop them into the oil in batches. (Popping them into the freezer for 30 minutes ahead of frying can help define the ridges in your churros.)
Fry the churros in batches for 3–4 minutes, until golden brown. Use tongs to transfer the fried churros to paper towel to drain. Toss with lots of cinnamon sugar. Serve with hot chocolate or coffee, and your choice of sweet gooey sauces for dunking into.