Adjust oven rack to lower-middle position and heat to 400 degrees. Heat oil in Dutch oven over medium heat until shimmering. Add onions, bell pepper, 1/2 teaspoon salt, and 1/4 teaspoon black pepper and cook until softened; about 5 minutes. Stir in garlic, 1 teaspoon oregano, and bay leaves and cook until fragrant; about 30 seconds.
Stir in eggplant, tomatoes and reserved juice, and chickpeas and reserved liquid and bring to a boil. Transfer pot to the oven and cook uncovered, until eggplant is very tender, 45 to 60 minutes, stirring twice during cooking.
Discard bay leaves. Stir in remaining 2 teaspoons oregano and season with slat and pepper to taste.