Season both sides of eggplant slices with 1 1/4 teaspoons salt; let stand at least one hour. Pat eggplant dry with paper towels, and sprinkle with pepper and remaining 1/2 teaspoon salt.
Heat oil in a large nonstick skillet over medium-high heat. Add eggplant slices; cook 3 minutes or until browned. Turn slices over. Cover, reduce heat to medium, and cook 25 minutes or until eggplant is soft.