Pick the parsley leaves and discard the stems (or save for stock). Blanch the leaves for 1 minute in boiling salted water. Drain the parsley in a colander and rinse with cold running water. Gently squeeze dry.
Put the blanched parsley in the blender with the court-bouillon and blend at high speed, stopping every 10 to 15 seconds to scrape the inside of the blender. Blend until the liquid is green and contains only tiny specks of parsley; this usually takes about 2 minutes.
Work the purée through a fine-mesh drum sieve with a plastic pastry scraper.
Heat the flavorful base in a saucepan and, just before serving, whisk in purée to taste.