In a pot, combine the water, butter, and sugar. Heat over medium while stirring until the butter has completely melted.
Next, add the flour and salt, and stir continuously with a wooden spoon to ensure everything is evenly mixed and forms a dough. Add the mashed banana and keep stirring until the dough begins to separate from the sides of the pot. Initially, the dough will be quite runny, but as you keep stirring over medium heat, it will thicken and pull away from the pot's sides.
Once this happens, remove the pot from the heat. Add the eggs one at a time, stirring constantly until each is fully incorporated. The dough should now be thick and smooth.
Transfer the dough into a piping bag fitted with a star nozzle.
In a pan, heat a generous amount of oil over medium-high heat (I used olive oil, but sunflower or vegetable oil work too). The oil should be between 180°C and 200°C. If it's too cold, the churros will absorb too much oil; too hot, and they'll cook too quickly and risk burning.
Carefully pipe the churro dough into the hot oil, cutting it into 4-5 inch pieces with scissors. Fry the churros for a couple of minutes on each side until golden brown.
Once they’re cooked, use a slotted spoon to remove the churros from the oil and place them on a paper towel to drain off excess oil.
I like to keep them in a preheated oven at 180°C while I cook the whole batch, so they stay warm.
Finally, coat your churros with cinnamon sugar and enjoy!