If you’re using frozen peas, defrost them entirely. Bring the water to a boil in a large soup pot, and add the coarse salt. Bring back to the boil and add the peas. Cook for anywhere from 5 minutes (for defrosted peas) or 13-17 minutes (for fresh peas). The cooking time for fresh peas will depend on a few factors, so taste a pea after 13 minutes and adjust the cooking time according to your tongue: the peas shouldn’t be pasty, but a distinct pea flavor should burst in your mouth when you bite.
Taking care to SAVE the cooking water, place a colander over a large bowl in the sink and drain the peas.
Place the peas back into the soup pot if you’re using a wand mixer, or in a blender (if you use a blender, the peas must be cool first). Add in 1⅓ cups (300 ml) of the cooking liquid. Using the wand mixer or blender, purée the soup until completely smooth. If the soup is too thick, you may add some more of the cooking liquid until you find the right consistency.
If you want a restaurant-caliber soup, strain it through a fine-meshed strainer, a china cap, or a chinois strainer. Then add the ½ cup of heavy cream and stir well. Once the soup is completely cooled, chill it in the refrigerator for at least one hour, and as long as overnight.
To make the cumin-pistachio garnish, dry-roast the cumin or cumin seeds in a very small cast-iron or other heavy-bottomed pan, stirring a few times. Remove the cumin from the pan as soon as you begin to smell the toasted cumin and let it cool completely. If using cumin seeds, grind them into a powder using a mortar and pestle or spice grinder.
Whip the heavy cream to medium peaks. Add the cooled cumin and the salt, and fold them in.
Divide the chilled soup into 4 soup plates, soup bowls, or any decorative cups (which you may also chill beforehand). Using two spoons to form small “dumplings” (quenelles) of whipped cream, or using a pastry bag fitted with a pastry tip, distribute the cumin whipped cream between the 4 soup cups.
Sprinkle with the chopped pistachios. Régalez-vous!