1Place diced eggplant in colander. Sprinkle with 2 teaspoons salt. Let stand 1 hour; rinse with cold water.
2In 10-inch nonstick skillet, heat 1/4 cup of the olive oil over medium-high heat. Cook half of the eggplant in oil until golden brown. Drain on paper towel-lined plate. Repeat with another 1/4 cup olive oil and remaining eggplant.
3In same skillet, heat remaining 1/4 cup olive oil over medium-low heat. Cook onions in oil about 10 minutes, stirring occasionally, until very tender. Add garlic and cook 30 seconds; add celery and cook 2 to 3 minutes. Add tomatoes; cook and stir 2 minutes. Add cooked eggplant, 1/2 teaspoon salt and the pepper; heat to a slow simmer. Cover; cook 20 minutes. Stir in parsley.