Heat oil in a 3- to 4-quart pan over medium-high heat. Add eggplant and cook, stirring often, until eggplant is very soft (8 to 10 minutes). Stir in garlic, tomatoes (break up with a spoon) and their liquid, tomato sauce, port, sugar, oregano, bay leaf, cinnamon stick, and all but 1 tablespoon of the parsley. Bring to a boil; then reduce heat, partially cover, and simmer until very thick (about 30 minutes). Season to taste with salt and pepper.