Line a 23 x 33 cm / 9 x 13-inch baking dish with parchment, leaving a little overhang on the long sides. In a 3-quart / 2.8 L heavy-bottomed saucepan, whisk the chickpea flour, fine sea salt, and black pepper into the 750 ml cold water until no lumps remain, then whisk in the olive oil.

Set the pan over medium-low heat and whisk constantly for 6 to 8 minutes, reaching into the corners, until the batter thickens to the texture of pudding and begins to bubble slowly.

Switch to a flat-edged wooden spoon and cook for 10 to 12 minutes more, stirring along the base, until the mass pulls away from the sides of the pan and no longer tastes raw. Lower the heat if it spits.

Scrape the hot batter into the lined dish right away and level it with a wet spatula to about 1.2 cm / 1/2 inch thick. Leave it uncovered at room temperature for 60 minutes, until it's firm and cool all the way through.

Heat the oven to 110 C / 230 F and set a wire rack over a sheet pan. Lift the slab out by the parchment and cut it into sticks about 2 cm wide and 8 cm long, trimming the ragged edges, to get about 40 sticks. Pat them dry with paper towels.

Pour the sunflower oil into a 28 cm / 11-inch heavy skillet and heat over medium-high until it reaches 175 C / 350 F.

Fry the sticks in 3 batches of 13 to 14, leaving a finger's width between them. Cook 3 to 4 minutes per side, turning once with tongs, until deep golden brown with a crisp shell.

Move each batch to the rack and sprinkle with flaky sea salt right away. Keep the rack in the oven and let the oil return to 175 C / 350 F between batches.

Serve within 20 minutes of frying, with lemon wedges, a grind of black pepper, and chopped parsley if you like.