Cut the eggplant, bell pepper, and onion into 1-inch cubes. Toss them in a large bowl with the garlic, olive oil, cayenne and salt and pepper. Spread them on a baking sheet. Roast for 45 minutes, until the vegetables are lightly browned and soft, tossing once during cooking. Cool slightly.
Place the vegetables in a food processor fitted with a steel blade, add the lemon juice and tahini, and pulse 3 or 4 times to blend. Taste for salt and pepper. Transfer to a bowl and add the chopped parsley. Garnish with extra parsley.