Oil a 12 by-8-inch baking pan and place a sheet of wax paper or parchment paper on the bottom.
Put the water, salt, pepper and olive oil in a saucepan, and bring to a simmer over medium heat. Gradually pour in the chickpea flour while whisking, once all the flour is in, whisk rapidly until the mixture is thick and most of the lumps have been worked out, like a thick pancake batter, about 1 minute. Take care to adjust the heat to so the batter doesn't boil or it will become too thick.
Immediately scoop the mixture into the prepared pan and smooth out with a small spatula. Lay another piece of wax or parchment paper on top and smooth with your hands to create a thin, even layer. Refrigerate until cool, about 30 minutes.
Meanwhile, whisk all the mayonnaise ingredients together. Refrigerate until ready to serve.
When chickpea mixture is set and cool, trim the edges and turn onto a cutting board. Cut lengthwise down the middle, then cut each piece into fries measuring about 4-by-1/2-inches, or cut into triangles or rounds with a cutter.
Heat about 2-inches of oil in a deep, heavy bottomed pot over medium heat until a deep-fry thermometer reads 375 degree F. Line a large plate with paper towels.
Working in batches, carefully slip the chickpea fries into the oil, and fry until crisp and golden brown, about 4 to 5 minutes per batch. Remove with a slotted spoon to the prepared plate. Serve the chickpea fries warm with the chipotle mayonnaise.
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