Grease an 8x8 inch (20x20 centimeter) baking dish and set aside.
Pour the water into a medium saucepan and bring to a boil.
Reduce heat to a simmer and add the olive oil, salt, and pepper.
Slowly whisk in the sifted chickpea flour.
Continue to whisk continuously, especially the bottom and sides, until the mixture starts to thicken.
Once too thick to whisk, switch to a wooden spoon and continue to stir until very thick and the mixture easily leaves the sides of the pan.
Remove from heat and immediately transfer the mixture evenly into the greased baking dish.
Smooth the top as much as possible with a spoon or spatula.
Cover the baking dish with plastic and refrigerate for at least 3 hours to overnight to set.
Once the chickpea mixture has completely set, carefully flip it out of the baking dish and onto a cutting board.
Use a sharp knife to cut the square in half, then slice batons about 1/2 inch (1.25 centimeters) thick.
Line a plate with paper towels and set aside.
Place a non-stick or seasoned skillet over medium heat and cover with a thin layer of olive oil.
Pan-fry the chickpea fritters in batches, taking care to not overcrowd, and turn until golden on each side.
Once golden on all sides, transfer to the paper-towel lined plate and repeat with remaining fritters. Add more olive oil to the pan as needed.
Serve the Panisses immediately while still warm with a sprinkling of salt and pepper.