Soak the chickpeas in plenty of water overnight. The following day, simmer the chickpeas in the soaking water for 1 hour. Remove the pot from the heat and let cool.
Drain the chickpeas. Peel and coarsely chop the garlic. Mash the chickpeas with the garlic, lemon juice, paprika, sesame seeds, 4 tablespoons of oil, and the parsley leaves until a thick paste has formed. Season to taste with salt and pepper.
Place the hummus on plates, and form a well in the center. Top with olive oil, to taste. Garnish with parsley leaves. Serve the hummus with the cucumber slices and the olives.