Cut 1/2 stick of butter (1/4 cup) into small pieces. Cut 1 stick of butter (1/2 cup) into small pieces, and set aside.
In a large bowl, beat the 1/2 stick (1/4 cup) butter and sugar with an electric mixer, about 2 min. Slowly add the eggs. Beat for 1 min. Mix in the key lime juice. The mixture will look curdled, but it will smooth out as it cooks.
In a medium, heavy-based, non-aluminum saucepan, cook the mixture over low heat until it looks smooth. (The curdled appearance disappears as the butter in the mixture melts.) Increase the heat to medium and cook, stirring constantly, until the mixture thickens, about 15 minutes. It should leave a path on the back of a spoon and will read 170°F on a thermometer. Don’t let the mixture boil.
Remove the mixture from the heat and transfer curd to a heat-safe bowl. Press plastic wrap on the surface of the lime curd to keep a skin from forming and chill the curd in the refrigerator. At this point, the curd is ready to serve as is, unless you would like to proceed with the lime cream instructions.