Put the eggplant cubes in a large colander and toss with a little salt. Place a plate directly on top of the eggplant with some sort of a weight on top of the plate (a jar, can, etc.). Set the colander in the sink or over a bowl and let drain away any bitter liquids for at least 30 minutes. Rinse away the salt under cold running water and pat the eggplant cubes thoroughly dry with paper towels. Afterwards, squeeze away any remaining liquid in the eggplant by the handful.

In a medium, deep pan over medium-high heat, heat about 2-inches of oil until hot, but not smoking, or when it reaches a temperature between 360°F and 375°F on a deep-fat thermometer. You can test the oil for readiness by dropping in a piece of eggplant and if it sizzles immediately it is ready. Working in batches, fry the eggplant until golden brown, about 3 to 4 minutes. Do not overcrowd the pan. Using a wire skimmer, transfer the eggplant to a paper towel lined plate to drain thoroughly.

In a 12-to 14-inch sauté pan over medium-low heat, combine the olive oil and garlic and gently sauté until the garlic softens and turns lightly golden. Raise the heat slightly and add the tomatoes to the pan. Simmer until the tomatoes begin to break down and release their juices, about 5 to 7 minutes, stirring and gently crushing the tomatoes with a wooden spoon. Add the eggplant and basil to the pan and toss briefly just to combine. Taste for salt and season, if necessary. Gently toss for about 1 minute longer just to blend the flavors.

Serve warm or at room temperature garnished with basil.