Heat the olive in a large pan over medium heat. Once the oil is hot, pat the eggplant cubes very dry then add to the pan. Working in batches, fry the eggplant until well browned and soft (about 10-12 minutes per batch) then remove to a paper towel-lined plate and sprinkle with salt.
Bring a large pot of salted water to boil.
Wipe the pan used to cook the eggplant down with paper towels then add the extra virgin olive oil, garlic, and anchovies. Saute for 2 minutes or until golden, while mashing the anchovies into the oil.
Add the red pepper flakes and cook for 30 seconds. Next, add the tomato paste and cook for 5 minutes stirring frequently. If the paste starts to burn, add a splash of water and turn down the heat a bit if required.
Add the crushed tomatoes to the pan and season with a bit of salt. Bring the sauce to a simmer.
Once the pasta water comes to a boil, cook the pasta until 1 minute less than al dente.
Add the pasta to the sauce and toss to coat. Add the eggplant cubes and the basil. Mix well and once the pasta reaches al dente remove the pan from the heat.
Taste test and adjust salt and pepper to taste. Serve in bowls, evenly distributing the ricotta salata cheese onto each plate. Enjoy!