Preheat grill or broiler.
Brush each eggplant slice generously with olive oil and sprinkle generously with salt.
Place the slices on the preheated grill. Cook on both sides until the eggplant is soft and pliable and has a nice char. Remove from grill and let cool. When the eggplant is cool enough to handle, coarsely chop and reserve in a large mixing bowl. Add the ricotta, vinegar, oregano, Parmigiano and crushed red pepper and stir to combine. Season with salt and reserve.
While the grill is still hot, grill the slices of bread on each side. When the bread comes off the grill rub each piece with a raw garlic clove and brush lightly with olive oil.
Top each piece of bread with the grilled eggplant mixture.