Bring a large pot of well salted water to a boil. Cook the penne according to package directions until al dente. Save ½ cup of the pasta water. Drain the penne, return to the pot, and set aside.
Meanwhile, heat the oil in a large skillet over medium-high heat until it shimmers. Add the eggplant and cook, stirring occasionally until it begins to soften, adding more oil if necessary, to prevent sticking, 5 to 6 minutes.
Lower the heat to medium, add the onions, and continue to cook, stirring occasionally until they begin to soften, about 6 minutes.
Add the garlic and cook until just fragrant, about 30 seconds. Add the chick peas, tomatoes, ¼ cup of the pasta water, 1 tsp. salt and ½ tsp. pepper and cook until just heated through, about 2 minutes.
Add the sauce mixture to the pot with the penne and toss until well combined. Add the remaining 1/2 cup pasta water if the mixture is too thick. Adjust the seasoning.
Divide the penne mixture among serving bowls. Top with the crumbled ricotta salata and basil and serve.