Place the chickpeas into a food processor and pulse until smooth. Add ⅓ cup tahini paste, lemon juice, grated garlic, and salt. Allow the food processor to run until everything is well incorporated and smooth.
Stream in the cold water and process again. If the hummus isn't creamy enough, add more water or a couple of ice cubes. You can also add olive oil to thin as necessary. The hummus should be slightly runny, as it will stiffen in the refrigerator.
At this point, taste the hummus and check for seasonings—add more tahini for bitterness, lemon juice for brightness, garlic for sharpness, or salt for flavor.
Once very smooth and velvety, add any spices or add-ins you'd like and pulse to combine. To serve, spoon the hummus onto a serving platter, using a spoon to make a swoop in the center of the dish. If desired, garnish with olive oil, paprika, parsley, more chickpeas, and serve.
Homemade hummus can be made and stored in the fridge for 2-3 days and up to one week, if kept properly. Hummus may also be frozen for up to 4-6 months (simply thaw in the fridge overnight before using).