Toss the eggplant with 1 teaspoon salt in a colander. Let it sit for 20 minutes to get out the excess moisture. Pat the eggplant dry with a towel.
Bring a large pot of salted water to a boil. Cook the pasta until al dente according to package instructions.
While the pasta is cooking, heat 1 tablespoon olive oil in a large skillet over medium high heat. Sauté the eggplant in 2 batches until it starts to brown and turn soft, about 3-4 minutes. Return all the cooked eggplant to the skillet.
Add the garlic and chilies to the eggplant, sautéing until fragrant, about 1 minute.
Stir in the tomatoes, 1 teaspoon salt, and pepper. Continue cooking the tomatoes, so they get juicy and wrinkled, about 3 minutes.
When the pasta is ready, use a slotted spoon to transfer it straight from the pot to the skillet. Stir it into the tomatoes and eggplant.
Finish the pasta with chopped parsley and shaved Parmesan before serving.