Place eggplant and bell pepper on a baking sheet and broil, 6 inches from heat source, until pepper is charred, about 20 minutes, turn often. Remove pepper and allow eggplant to continue cooking until very soft, about another 10 minutes. Remove and let cool until able to handle.
Peel the pepper, remove stem and seeds, and chop. Scoop pulp and seed out of eggplant; set aside.
Heat oil over medium heat in a nonstick pot, sauté garlic, leeks, and onions until softened, about 5 minutes. Stir in broth, tomatoes, tomato paste, and bay leaves; bring to a boil. Lower heat, cover and cook 10 minutes.
Add soup to a food processor or blender with chopped peppers, eggplant pulp, and milk; puree.