Preheat the oven to 425°F.
Clean and chop the eggplant into ¾ to 1 inch chunks and place in a large bowl.
Shake 1½ teaspoons of salt with 1½ ounces of water in a small tightly lidded jar, dissolving the salt.
Add 1½ ounces of extra virgin olive oil to the jar and shake vigorously to emulsify the water and oil.
The emulsion won't be stable for long. Quickly pour the salt, water and oil mixture over the eggplant and stir to uniformly coat the eggplant pieces with the mixture.
Let the eggplant rest in the oil and brine for 15 minutes, then spread the eggplant evenly over a baking sheet.
Roast the eggplant in the 425°F oven for 30-40 minutes. The eggplant should be browned, especially the side that is in contact with the pan. The edges should be firm, but the cubes are soft with a custardy interior.
Meanwhile heat water to cook the pasta in one pot and heat the pasta sauce in a second pot that is large enough to hold the sauce, cooked pasta and eggplant.
Salt the water and cook the pasta according to the package directions.
Stack the basil leaves and slice into thin julienne strips. Add half the basil to the hot pasta sauce, reserving the rest for topping.
Fold the roasted eggplant into the hot pasta sauce, then stir in the cooked and drained pasta.
Plate the pasta and top it with the reserved basil and the grated cheese.