Place a pot of water on the stove to boil for pasta.
Trim half of the skin from the eggplant. Leaving a little skin on will add color and texture to the dish. The small, firm eggplants are not too bitter and when they are firm, they will not soak up as much oil, so they do not need to be salted and pressed. However, if you leave all the skin, especially when you use baby eggplant, the skin overpowers the flavor of the flesh and the texture is too tough overall.
Heat a medium nonstick skillet over medium-high heat. Cut the eggplant into 1-inch-by-1/2 inch bite size pieces. Add 2 turns of extra-virgin olive oil to the pan, the garlic and the eggplant. Turn and toss the eggplant and season it with salt and pepper. Let it brown lightly at edges, about 5 minutes, then reduce heat to medium low and continue to cook.
Add salt and ravioli to the pasta water and simmer to package directions, about 5 or 6 minutes, until just tender.
While the pasta cooks, dice tomatoes and add them to the cooking eggplant. Adjust seasoning with salt and pepper.
Drain cooked pasta and plate individually or on a platter. Top with eggplant and tomatoes and all of the basil and cheese. If you plate individually, use 1/4 of the basil and 2 ounces of cheese, crumbled, per portion.