Prepare an ice-water bath; set aside. Bring a medium pot of water to a boil; stir in 1 tablespoon salt. Add chervil. Return to a boil; cook until bright green, about 30 seconds. Using a slotted spoon, immediately transfer to ice-water bath. Drain, and chop coarsely.
Process chervil with 1/4 cup cold water in a food processor until very finely chopped. Pour through a fine-mesh sieve; discard liquid. Whip cream in a medium bowl until thick and fluffy but still pourable; stir in chervil, and season with salt.