Place the chickpea flour and salt in a large pot over medium-low heat, slowly incorporating the water whilst whisking, until you have a smooth batter with no lumps.
Cook the panelle mixture over medium heat, stirring constantly with a wooden spoon or whisk for about 10-15 minutes, until the mixture thickens and becomes like a very thick potato mash, and pulls away from the sides of the pan. Whisk in the chopped parsley and remove the pan from the heat.
Line a baking tray with parchment paper. Spread the hot chickpea mixture onto the prepared baking sheet to a thickness of about ¼ inch ( 0.5 cm), using a long knife or spatula to leven out the surface. Allow it to cool and set for about 30 minutes.
Once the panelle mixture has cooled and set, use a knife to cut it into strips or squares. Traditionally, they are cut into rectangular shapes.
Heat the sunflower oil in a deep frying pan or skillet over medium-high heat until it reaches 175℃/ 350℉. You want enough oil to submerge the panelle.
Carefully fry a few panelle at a time until they are golden brown and crispy, about 2-3 minutes per side. Use a slotted spoon to remove the panelle from the oil and place them on a plate lined with paper towels to drain any oil in excess.
Sprinkle the panelle with some sea salt and serve them straight away, with lemon wedges on the side, or in a sandwich.