Cut off and discard stem and bottom end of the eggplant. Cut eggplant crosswise into 3/4-inch slices, then cut slices into 3/4-inch strips.
Place strips in a colander, sprinkle with salt, and toss. Set colander over a bowl or in the sink and let eggplant stand for at least 1 1/2 hours, preferably for 2 to 3, stirring it a couple of times. Rinse eggplant under cold, running water, rubbing the strips lightly in your hands. Shake colander to drain. Lay strips on a triple thickness of paper towels; cover with another triple layer of towels.
Using your palms, press each eggplant strip very firmly until it looks green and translucent and feels firm and leathery when pressed between fingertips. Repeat pressing process on fresh toweling if eggplant has not yet reached this stage. Repeat with remaining eggplant strips.
Heat the oil in a large, heavy saute pan to 360 degrees F.
Combine flour, salt, turmeric, cayenne and coat eggplant batons with the mixture, shaking off any excess. Place as many of the batons in the pan as will fit loosely without overcrowding. Fry, turning, until golden brown, about 2 minutes. Remove from the pan with a slotted spoon and transfer to paper towels to drain. Season with salt.