Bring a large 10- to-12-quart pot of water to a boil over high heat.
Preheat a grill (wood, charcoal or gas) to medium-high direct heat, or, alternately follow this recipe using an indoor stovetop. (Please note, if cooking on a grill, be sure your pan is heavy-bottomed and doesn't have plastic handles.)
Add the oil to a large pan set on the grill grate. Once hot, add the onions and saute until soft, but don't let them brown. Add the red pepper flakes and cook until fragrant, but don't let them burn. Add the crushed tomatoes and sprinkle with salt and pepper. Simmer the sauce on a medium-low flame, about 20 minutes. Thrive for balance in the consistency of the sauce; it has to be fluid, but it should not look wet. If the sauce is liquidy, cook it a bit more.
Meanwhile, sprinkle the eggplant slices with salt and pepper. Drizzle the eggplant with some oil, and grill in batches, until they are marked by the grill and cooked through, 2 to 3 minutes per side. Transfer the eggplant to a large plate or sheet tray and allow to cool slightly. Slice the grilled eggplant into smaller, bite-size pieces. Add the eggplant to the sauce, along with the bay leaves.
Once the pot of water is at a boil, and the sauce has been simmering, add the 2 tablespoons salt to the water. Add the rigatoni. Cook until al dente, then drain well. Add the rigatoni to the sauce and toss.
Remove the bay leaves before serving. Serve with basil and Parmigiano-Reggiano at the table as an optional garnish for guests.