Place chickpeas in a bowl of water and rub them together to peel the skin (optional step, but helps create a creamy texture).
Drain the garbanzo beans and transfer them to a food processor. Blend them alone until they become powder-like, scraping down the sides as needed.
While the food processor is running, add the ice cubes, lemon juice, tahini, garlic clove and salt, and blend for about 5 minutes until smooth. Taste and adjust as needed by adding more lemon juice or salt.
Spoon the hummus onto a plate or bowl, and spread the hummus with the back of a spoon to create swirls.
Drizzle with olive oil, sprinkle with paprika and fresh parsley. Serve cold or at room temperature.