About 30 to 60 minutes before starting to cook, salt the chopped eggplant in a sieve, toss until covered, and let sit in the sink.
2 medium Japanese eggplants or one small globe eggplant, roughly chopped into half inch pieces (no need to peel), salt for sweating and to taste
When ready to cook, rinse off the salt and pat some of the water off with a paper towel or kitchen towel. You can even get rid of a bit more of the water out by squeezing the eggplant gently (but there's no need to squeeze like you are making latkes).
Using a large (12 inch) skillet that has a lid, heat the olive oil over medium-low heat, and then cook the onion for about 5 minutes until starting to soften.
1 tablespoon olive oil, ¼ cup yellow or white onion, chopped fine
Add the eggplant and cook, stirring occasionally, until the eggplant is starting to brown (about 5 minutes)
Add the garlic and olives and cook, stirring, for one minute.
2 cloves garlic, 10-12 Kalamata olives, pitted and coarsely chopped
Add the canned tomatoes, tomato sauce, and red pepper flakes and stir to combine.
28 ounce can chopped tomatoes, ¼ cup homemade or store bought tomato sauce, 1 pinch red pepper flakes
Add the broken lasagne noodles as a top layer (do not stir them in), cover the pan, and let simmer with occasional bubbles for about 10 minutes.
12 no-boil lasagne noodles, broken up roughly
At about the 10 minute mark, stir in the noodles and continue to let the mixture cook, covered and at a simmer, for about another 10 minutes until the noodles are soft. Stir occasionally to prevent sticking.
Add in salt and pepper to taste (I start with ½ teaspoon of salt and ¼ teaspooon of pepper).
salt and pepper to taste
Remove from heat and stir in the chopped mozzarella and the Parmesan, reserving a tablespoon or two of the Parmesan for serving.
½ pound fresh mozzarella, chopped, 1 ounce Parmesan, grated, plus more for topping
Add the ricotta in large (about 2 tablespoon) dollops around the pan, but don't stir in. Cover the pan and let it sit for 5 minutes.
1 cup ricotta cheese
Sprinkle with basil and Parmesan and admire your handiwork before serving.
¼ cup fresh basil, chopped