In a blender, add the cooked and peeled chickpeas, half the tahini, half the lemon juice, the garlic and the 2 tablespoons of cold water.
Blend for 2 to 4 minutes, then add the remaining tahini and lemon juice, adjusting to taste.
Continue blending, then check texture. Then add the ice cubes one at a time, stopping the blender to check the consistency.
Note: Add ice cubes and/or cold water in stages to obtain a creamy hummus without liquefying it.
When you have achieved the right texture, add salt to taste.
Transfer the hummus to a serving plate. Make a slight well in the center, leaving the center raised.
Place the reserved chickpeas in the center and generously pour olive oil around them. Garnish with paprika, cumin and fresh parsley, if desired. Sprinkle the chickpeas with a little sumac or Espelette pepper.
Serve with pita bread, nachos or breadsticks and/or crunchy vegetables.