Preheat oven to 375ºF and preheat a grill to medium-high.
Place a medium pot over medium-high heat with 2 turns of the pan of EVOO, about 2 tablespoons. Add the onion and garlic to the pan, and cook until tender, 3-4 minutes. Add the tomatoes to the pan and break them up with a wooden spoon or potato masher. Add the cinnamon stick, salt, pepper and the basil to the pan, and simmer the sauce until thickened and aromatic, about 10 minutes.
While the sauce is simmering, brush the eggplant slices with the remaining EVOO and grill them until marked and tender, about 5 minutes per side.
Meanwhile, combine the ricotta, 1 cup Parmigiano Reggiano and egg yolks together in a medium bowl. Reserve.