This sauce must be used immediately. It does not refrigerate well. /This modern sauce has a subtle flavor that’s ideal for serving with seafood or even hard-cooked eggs. The sauce will break easily so when serving over hot foods, serve it separately so the diners can add it just before they eat.
Cook the fennel in boiling, salted water for 10 minutes. Drain well. Purée the fennel with a stick blender fitted with a chopping blade or in a small food processor. Force the mixture through a fine sieve to remove any chunks of fennel remaining.
Put the puréed fennel in a small saucepan over medium heat. Dry the purée while stirring to prevent the fennel from burning. When mostly dry, chill thoroughly.
Place the chilled fennel purée in a bowl along with the mustard, egg yolk, and lemon juice. Whisk until smooth. Whisk in the olive oil. Season with salt and pepper.