Add the chickpeas, tahini, lemon juice, salt, garlic, olive oil and basil leaves to the bowl of a food processor.
Blend well for about 4-5 minutes, stopping to scrape down the edges a few times. The hummus should already look pretty smooth.
Add ice cubes one at a time, blending after each addition. The hummus will start to look even smoother and will turn a lighter shade as the tahini reacts with the cold ice. Keep adding ice cubes and blending to desired consistency. This can take about 5 minutes. Season with salt and pepper to taste.
Serve or store covered in the fridge until needed.
Notes
Substitutions - I use chickpeas that I cook from dried chickpeas and I remove the skins off of them as they will give you the smoothest texture. Use canned if you prefer but the texture won't get quite as smooth - it'll still taste delicious.