Bring a large pot of salted water to boil for the pasta.,

Brush a 9-by-13-inch baking dish with olive oil.,

Preheat oven to 425 degrees F.,

Use a vegetable peeler to remove vertical stripes from the eggplant.,

Cut the eggplant into 1 inch cubes.,

Heat a large nonstick skillet over medium high heat.,

Add enough vegetable oil to film the bottom of the pan.,

Add half of the eggplant and season with salt.,

Cook, tossing occasionally, until browned and almost tender, 6 to 7 minutes.,

Repeat with the remaining eggplant.,

Carefully pour the oil out of the skillet and wipe it clean with a paper towel.,

Return the skillet to medium heat.,

Add the olive oil.,

When the oil is hot, add the onion and cook until softened, about 4 minutes.,

Add the tomatoes, red pepper flakes and 1 cup water.,

Season with salt.,

Bring to a simmer and cook until slightly thickened, about 10 minutes, adding the eggplant cubes in the last 5 minutes.,

Stir in the basil.,

Meanwhile, add the ziti to the boiling water and cook until al dente.,

Drain and return to the cooking pot.,

When the sauce is ready, pour over the pasta and toss to combine.,

Add the ricotta and stir gently to distribute.,

Transfer the pasta to the oiled baking dish.,

Combine the provolone and Grana Padano in a small bowl and sprinkle over the pasta.,

Bake the pasta until browned and bubbling, 20 to 25 minutes.