Cover bottom and sides of each of 2 largecolanders with 1 layer of eggplant slices;sprinkle generously with coarse salt.Continue layering eggplant slices in eachcolander, sprinkling each layer with coarsesalt, until all eggplant slices are used.
Placeeach colander over large bowl; let standat least 30 minutes and up to 1 hour. Rinseeggplant slices to remove excess salt; drythoroughly with paper towels.
Position oven rack 5 to 6 inches fromheat source and preheat broiler. Line 3 largerimmed baking sheets with parchmentpaper. Arrange eggplant slices in singlelayer on prepared baking sheets.
Brush bothsides of eggplant slices with olive oil. Broil1 sheet at a time until eggplant slices aretender and beginning to brown, watchingclosely and removing eggplant slices asneeded if cooking too quickly, 3 to 4 minutesper side.
Remove baking sheet from ovenand cool eggplant while preparing filling.
Bring large pot of salted water to boil.
Add chard to pot and boil just until tender,about 2 minutes.
Drain; rinse with coldwater. Squeeze chard very dry, then chopcoarsely. Squeeze chard dry again betweenpaper towels.
Whisk eggs and pinch ofcoarse salt in medium bowl. Stir in choppedchard, ricotta cheese, 1 cup Parmesan, mint,and black pepper.
Lightly oil 15 x 10 x 2-inch glass bakingdish.
Spread half of tomato sauce evenlyover bottom of dish. Divide chard-ricottafilling among eggplant slices, placing about1 heaping tablespoon filling in center ofeach. Starting at 1 short end of each, looselyroll up eggplant slices, enclosing filling.Arrange rolls, seam side down, atop saucein baking dish. Spoon remaining tomatosauce over.
Place mozzarella slices in singlelayer over rolls.
Sprinkle with remaining1/4 cup Parmesan cheese. DO AHEAD: Can bemade 1 day ahead. Cover with foil and chill.
Preheat oven to 350°F.
Bake eggplant
Parmesan rolls, covered with foil, untilheated through, about 30 minutes if freshlymade or 40 minutes if refrigerated. Uncoverand bake until brown in spots and sauce isbubbling, 15 to 20 minutes.
Serve hot.
* Available at many supermarkets and atspecialty foods stores and Italian markets.Regular mozzarella can be substituted.