Using a high-powered blender, combine the lime juice, white fish, fish stock, onion, celery, garlic, ginger, aji paste, cold water, and chopped cilantro stems.
Blend on high power for 5 minutes, or until completely smooth.
Add the salt and ⅓ cup of ice cubes.
Blend again on high for another 60 seconds.
Place a sieve over a large mixing bowl.
Pour the blended mixture into the sieve and let the liquid drip into the bowl.
Discard the remaining pulp in the sieve.
Cover the bowl and refrigerate until ready to use.
Store in the refrigerator for up to 24 hours, or freeze in an airtight container for up to 1 month.