Place the chickpeas in a large bowl and add enough cold water to cover. Cover with plastic wrap and let soak for at least 8 hours or overnight. Drain the chickpeas and transfer to a large pan. Cover well with water and bring to a boil. Boil vigorously for at least 10 minutes, then reduce the heat and let simmer for 1 1/4 hours, or until tender. Skim away any surface scum if necessary. Drain and let cool. Place the garlic, oil, sesame seed paste, lemon juice, and cayenne in a food processor and blend until smooth. Add the chickpeas and process to a thick puree, adding a little water to thin the mixture if necessary. Season to taste with salt and pepper. Transfer to a serving bowl, cover with pastic wrap, and let chill until required. When ready to serve, garnish with parsley sprigs and serve with pita breads filled with fresh salad greens and cucumber and tomato slices.