Grease a rimmed sheet tray or your kitchen counter with olive oil.
Add the chickpea flour, 1 1/2 teaspoons salt, the pepper and 3 cups water to a medium saucepan set over medium heat and whisk until smooth. Cook, stirring constantly with a wooden spoon, until the mixture is very thick (almost like polenta); this should take around 10 minutes or so. Stir in the parsley. Spread the mixture smoothly in the sheet tray or spread evenly on your kitchen counter. Let cool until firm, about 1 hour.
Heat 1/2 inch grapeseed oil in a heavy-bottomed high-sided skillet or Dutch oven until hot. Test the heat of the oil with the handle of a wooden spoon. Place the spoon into the oil and if it bubbles, the oil is ready.
Cut the panelle into small triangles or thin strips. Fry in batches until lightly golden, about 2 minutes per side. Drain on a sheet tray lined with paper towels. Season with a touch more salt.
Serve on brown-paper-lined plates garnished with a sprinkling of chopped parsley.