Preheat the oven to 400 degrees.
Scatter the pistachios evenly onto a sheet pan and bake until lightly toasted and fragrant, for 5-7 minutes.
Place ½ cup of the hot pistachios and the oil into a mini food processor and process, scraping down the bottom and sides, as needed, to form a paste.
Add the chickpeas, tahini, parsley, lemon juice and ½ cup of cold water and process until smooth, adding up to an additional ½ cup of water, to achieve desired consistency.
Season with salt, to taste.
Transfer the hummus to a serving bowl and use a spoon to create wells.
Drizzle extra virgin olive oil into the wells.
Rough chop the remaining pistachios and sprinkle over the hummus along with the pomegranate arils; serve with crudité or pita chips.