Scrape and thoroughly clean the mussels under cold running water, discarding any that remain open. Drain well.
In a large casserole, bring the sweet cider to a boil over high heat. Add peeled and finely minced shallots; simmer for 3 minutes.
Add mussels and toss gently with a slotted spoon until they open. Remove with a skimmer to a serving dish and cover to keep warm.
Pour half the cream into the cooking liquid; reduce over high heat for 5 minutes. Strain through a chinois or muslin into a clean saucepan.
Whisk egg yolks with remaining cream. Stir into the sauce over low heat, whisking until thickened—do not boil. Season lightly with salt and Espelette pepper; adjust to taste.
Drizzle sauce over mussels, sprinkle with chopped flat-leaf parsley, and serve immediately.
