Prep the eggplant. Peel the eggplants and dice in ½ inch cubes. Spread the eggplant over a sheet tray lined with a clean kitchen towel or paper towels. Very generously salt the eggplant and cover with another clean kitchen towel or paper towels. Cover with another sheet tray and place in the fridge with heavy items on top of it overnight or to 48 hours.
Prep the sauce. In a large bowl or container, combine the diced tomatoes, olive oil, white wine, salt, pepper, garlic, and basil. Cover and let it sit at least an hour or overnight for the best flavor.
Cook the pasta. Set a large pot of water to boil. Season generously with salt. Cook the pasta according to the package directions or until al dente. Reserve ½ cup pasta water before draining.
Sauté the eggplant. In a large skillet, heat ⅓ cup olive oil over medium high heat until it shimmers. Add the eggplant and season with a pinch of salt and pepper. Cook for 8 to 10 minutes until browned, stirring every 2 minutes or so.
Make the sauce. Add the fresh diced tomato sauce to the pan and let it simmer for about 2 minutes to cook off the alcohol in the wine. Stir in the cooked pasta, smoked cheese, and ¼ to ½ cup of the reserved pasta water depending on how much liquid you would like your sauce to have. Sauté all the ingredients together, remove from heat, and serve immediately.