Place cubed eggplant in a strainer and toss with kosher salt. Let sit for 20-30 mins. The salt will draw out the moisture from the eggplant so that it doesn't absorb as much oil when sauteing and making it more tender and milder in taste.
In a large, deep saute pan (you will make the sauce in the same pan), heat 2 tablespoons olive oil over medium high heat until shimmering, not burning. Add eggplant, saute, stirring frequently for approximately 10 minutes or until tender and browned. If eggplant is sticking to the pan, add a touch more olive oil.Turn off heat and transfer eggplant to a plate and set aside.
Let skillet cool a few minutes and wipe clean of any residual eggplant if desired.
If you have excess oil from the egpplant, you can use that oil. Otherwise. heat 2 tablespoons olive oil over medium heat until shimmering, not burning. Add garlic, anchovies and crushed red pepper flakes. Using a wooden spoon gently saute and stir all while mashing/ breaking up the anchovies, approximately 2-3 minutes. Stir in tomatoes and bring to a simmer. Simmer, stirring occasionally for 10 minutes till well combined and thickened.
Meanwhile, boil pasta water so that you can cook pasta when the eggplant goes in to the sauce.
Add sauteed eggplant to the tomato sauce. Stir to combine and let cook 5 minutes for flavors to meld.
Stir fresh basil into sauce. Let cook an additional few minutes.
Taste and season with additional salt and crushed red pepper to taste.
Cook pasta al dente or to taste, reserving 1/2 pasta water before draining
Place cooked and drained pasta back into the pot it was cooked in. Add sauce to the pasta and toss to combine adding reserved water as needed to get desired consistency.
Serve into bowls, top with fresh basil and ricotta salata. Enjoy!