In a medium-sized mixing bowl, beat butter, sugar, and salt until smooth.
Mix in the eggs and egg yolks one at a time until just combined.
Mix in the carrot juice and ginger. The mixture may separate a little at this point and that is fine.
Transfer the mixture to a small pot on medium-low heat. Stir regularly until the mixture reaches 175 F on a candy thermometer, about 20 minutes. It should be bubbling periodically, but not a fast-paced boil.
Remove from the heat and strain out any clumps with a fine sieve. Press plastic wrap directly onto the surface of the curd and poke a few holes in it to let the steam release. Refrigerate until ready to use.
Stays fresh for up to one week in the refrigerator.Yield: 12.5 ounces