Eggplant Caponata

Peel 2 lb. small Italian eggplants, leaving some strips of peel, then cut into 1" cubes and spread on half of a kitchen towel. Sprinkle eggplant with 1 Tbsp. Diamond Crystal or 1¾ tsp. Morton kosher salt (or 2 tsp. fine sea salt), then cover with other half of towel and weight with a baking sheet topped with 2 or 3 large cans for 30 minutes.

Meanwhile, heat ½ cup extra-virgin olive oil in a 10" heavy skillet over moderately high heat until hot but not smoking, then cook 1 medium onion, chopped, stirring, until pale golden, 6–8 minutes. Add 4 medium celery ribs, thinly sliced and cook, stirring, until onion and celery are deep golden brown, about 10 minutes. Add ⅓ cup large green Sicilian olives, pitted and coarsely chopped, ⅓ cup Italian capers packed in salt, rinsed well, and 2 Tbsp. sugar and cook, stirring, 2 minutes, then stir in ⅓ cup white wine vinegar and 1 (14–15 oz.) can whole tomatoes in juice, drained and chopped.

Reduce heat and simmer, covered, stirring occasionally, 20 minutes. If sauce is very acidic, add 1–2 tsp. more sugar (to taste). Transfer to a bowl and keep warm, covered.