Halve eggplant lengthwise, then cut crosswise into 1/2-inch slices.
Combine egg and 1 tablespoon water.
Combine crackers, parsley, 1/2 teaspoon salt, and 1/8 teaspoon pepper.
Dip eggplant in egg mixture, then in cracker mixture'.
Cook eggplant in hot oil till tender and golden, 2 to 3 minutes per side.
Drain on paper toweling.