Bring 4 quarts of water to a rolling boil in a large pot. Add the eggplant pieces and return to a boil. Reduce the heat and simmer until the eggplant pieces are tender, about 10 minutes.
Drain the eggplant pieces on paper towels. Poke holes in the flesh with a fork and squeeze out the excess liquid, a few pieces at a time, between 2 clean paper towels. Roughly chop the eggplant and season with salt and pepper.
Place the warm eggplant into a bowl with 2 eggs, the grated cheese, parsley, currants, pine nuts, and 3/4 cup of the bread crumbs. The resulting mixture should be moist, but not wet. Add some more bread crumbs if necessary.
Beat the remaining 2 eggs in a bowl. Drizzle with extra-virgin olive oil and salt, to taste. Shape the eggplant mixture into small balls about 1 1/4 inches in diameter (like a golf ball). Coat each bowl with the egg and then roll the ball in bread crumbs. Let the breaded balls rest for 10 minutes before frying.
Fill a deep pot no more than halfway with extra-virgin olive oil. Heat oil over medium-high heat until it reaches a temperature of 360 to 365 degrees F. The oil should remain at or around this temperature throughout the cooking process. Working in batches of 6, fry the eggplant balls until golden brown. Use a slotted spoon or spider to gently drop the balls into the oil, being careful not to splatter the hot oil. Using the same spoon or spider, remove the finished balls, and drain them on paper towels.
In a 12-inch saucepan add the tomato sauce. Lay eggplant balls into sauce and add the fresh chiles. Over medium-low heat, simmer for 30 minutes, gently stirring occasionally. Sprinkle with the fennel tops and serve at room temperature.
In a 3-quart saucepan, heat the olive oil over medium heat. Add the onion and garlic and cook until soft and light golden brown, about 8 to 10 minutes. Add the thyme and carrot and cook 5 minutes more, until the carrot is quite soft. Add the tomatoes and juice and bring to a boil, stirring often. Lower the heat and simmer for 30 minutes until as thick as hot cereal. Season with salt and serve. This sauce holds 1 week in the refrigerator or up to 6 months in the freezer.