Step 1Place the soaked and drained chickpeas in a saucepan and cover with plenty of fresh water. Bring to a boil; skim, add one-half teaspoon salt, cover, and cook over medium heat, about 1 1/2 hours, until the chickpeas are very soft.
Step 2Meanwhile, crush the garlic and one-half teaspoon salt in a mortar until pureed. Transfer the puree to the work bowl of a food processor, add the sesame seed paste and lemon juice and process until white and contracted. Add one-half cup cold water and process until completely smooth.
Step 3Drain the chickpeas, reserving the cooking liquid. Add the chickpeas to the sesame paste mixture and process until well blended. For a smoother texture, press the mixture through the fine blade of a food mill. Thin to desired consistency with reserved chickpea liquid. Adjust the seasoning with salt and lemon juice. (The hummus can be kept in a tightly closed jar in the refrigerator for up to a week.) Serve chilled or at room temperature; sprinkle with a pinch of paprika and parsley and drizzle with oil.