Place the chickpea flour, water, and salt in a medium sized sauce pan and whisk until smooth. Set over medium heat, and whisk constantly as the mixture slowly heats. Cook and keep whisking, scraping the bottom and sides of the pan frequently, until the mixture is smooth, thick and starts to pull away from the sides of the pan, about 5 minutes. Remove from heat and stir in the parsley.
Pour the mixture onto a parchment covered baking sheet (approximately 12” x 15”) and spread it quickly with a spatula, before it cools and sets, so it fills the pan in an even layer, about ¼ inch thick. Let cool in the refrigerator for approximately an hour, until completely firm.
Once cooled, cut into squares with a sharp knife. Carefully lift the cut pieces from the pan with a spatula or your hands.
To fry the panelle, pour enough canola oil into a wide heavy skillet to cover the bottom to a depth of 1/2 inch, and set over medium heat. When the oil is hot, fry the panelle about 3 minutes, until the underside is crisp and golden, then flip and brown the other side about 2-3 minutes more.
Place the panelle on paper towels to drain excess oil. Drizzle lightly with salt and serve hot. The panelle may also be served in a panino.