Cut eggplant into 1-inch cubes. Dust with 1 tablespoon salt and allow to drain in a colander.
Meanwhile, in a little olive oil, saute celery, carrot, and yellow onion for about 15 minutes. Use a large frying pan for this. Then saute the drained eggplant for 10 minutes in a little oil.
Place all of these in a heavy 2-quart kettle and add wine vinegar, sugar, canned tomatoes (mashed), tomato paste, green olives, capers, and anchovies, and let all of this simmer for 15 to 20 minutes. Add salt and pepper. Chill and serve.