Combine the chickpeas, tahini, garlic, lemon juice, cumin, and salt in a food processor.
Blend the mixture until roughly combined.
With the food processor running, slowly drizzle in the olive oil and ice water until the mixture becomes completely smooth and creamy.
Transfer the dip to a serving bowl, garnish with chopped parsley, sumac, and an extra drizzle of olive oil. Serve immediately with cucumber and bell pepper slices.