In a medium heavy-bottomed saucepan, whisk together the chickpea flour, water, salt, and optional black pepper and chopped parsley until smooth and lump-free.

Place the saucepan over medium heat and cook, stirring constantly with a wooden spoon or whisk, for 5-7 minutes, until the mixture thickens considerably and pulls away from the sides of the pan, forming a thick paste.

Immediately spread the hot mixture evenly onto a parchment-lined baking sheet or several flat plates, about 1/4 inch (0.6 cm) thick. Ensure it's as flat and smooth as possible.

Let the mixture cool completely and firm up, which will take about 30 minutes at room temperature. Once firm, cut the panelle into desired shapes, typically rectangles or diamonds.

Heat the vegetable oil in a deep frying pan or skillet over medium-high heat to 350-375°F (175-190°C). If you don't have a thermometer, a small piece of panelle should sizzle immediately when dropped in.

Carefully fry the panelle in batches, being careful not to overcrowd the pan. Fry for 2-3 minutes per side, or until golden brown and crispy.

Remove the fried panelle with a slotted spoon and place them on a plate lined with paper towels to drain excess oil.

Serve the panelle immediately while hot, accompanied by fresh lemon wedges for squeezing over.