Stir in broth, tomatoes, oregano, basil, salt, black pepper, and the browned eggplant, then bring to a boil over medium-high. Cover, adjust heat to medium and cook, stirring occasionally, until eggplant is very tender, 15 minutes. Uncover and cook, stirring and mashing half of the eggplant, until sauce is thickened, 2 minutes.