Step 1Peel eggplant. Cut it lengthwise into 1/2-inch thick slices. Salt slices on both sides and arrange them in 2 stacks of equal height in large shallow bowl. Place an upside-down plate on top. Press eggplant under a light weight, such as a can of tomatoes or a salt box, for 2 hours to express bitter liquid.
Step 2Rinse eggplant of excess salt under a trickle of cold running water. Pat dry with paper towels and layer slices on platter with 2 sheets of paper towels between each layer.
Step 3Heat oil in heavy 9-inch skillet over medium heat until very hot. Fry eggplant in batches until rich golden in color and cooked through, 2 to 3 minutes each side. Drain excess grease on paper towels.
Step 4When eggplant has cooled to room temperature, cut into 2 1/4-inch strips. Spread strips on paper towels to further absorb grease until needed.
Step 1Place food mill fitted with smallest-holed disk over bowl. Pour tomatoes and their liquid into mill. Puree to remove seeds, which can make sauce bitter. Scrape pulp from bottom of mill into bowl.
Step 2Place onion and oil in heavy medium pot over medium heat and saute onion until it turns translucent, about 5 minutes. Stir in dissolved tomato paste. Let it thicken about 1 minute and add tomatoes. (tomato puree? kg) Season with pepper to taste and add sugar and basil. (Do not salt sauce as there is enough salt in the eggplant and ricotta salata.) Reduce heat to low and simmer sauce, uncovered, stirring from time to time, until sauce thickens, 40 minutes. Do not let it boil.
Step 1When sauce has completed its cooking time, cook pasta in plenty of rapidly boiling salted water until al dente, about 10 minutes.
Step 2About 5 minutes after pasta begins cooking, place eggplant pieces in sauce to get hot. When pasta is cooked, drain thoroughly and place in warmed serving bowl. Toss with sauce and eggplant, and with ricotta salata. Serve very hot with additional freshly ground pepper to taste.