Cut the eggplant into 3/4-inch cubes. Place the cubes in a colander and sprinkle them generously with kosher salt. Allow the eggplant to sit for about 15 minutes. Rinse the eggplant, then pat it as dry as possible with a tea towel or paper towels.
Bring a large pot of salted water to a rolling boil. Add the pasta and cook according to package instructions.
While the water is reaching a boil and pasta is cooking, heat the olive oil in a large, deep skillet over medium high heat. Add the eggplant. Cook, stirring from time to time, for 8-10 minutes, or until the eggplant is crisping at the edges and tender in the center.
Add the garlic to the skillet. Cook, stirring constantly, for a minute, or until the garlic is quite fragrant. Stir in the tomatoes, capers, and basil. Bring the sauce to a simmer, and then reduce the heat to low. Simmer the pasta sauce, uncovered, for 5-10 minutes, or until it has thickened up considerably. Add kosher salt and crushed red pepper to taste.
When the pasta is ready, drain it, reserving 3/4 cup of the pasta cooking water. Add the drained pasta to the sauce. Stir well, then add a little of the pasta water to loosen the mixture up.
Divide the pasta into serving bowls and top each portion with extra basil and vegan cheese, if desired. Serve right away.