Add chickpeas and minced garlic to the bowl of a food processor. Puree until a smooth, powder-like mixture forms.
While processor is running, add ice cubes, tahini, salt, and lemon juice. Blend for about 4 minutes or so. Check, and if the consistency is too thick still, run processor and slowly add a little hot water. Blend until you reach desired silky smooth consistency.
Spread in a serving bowl. Add a few chickpeas to the middle, if you like. Enjoy with warm pita wedges and your favorite veggies.