In a small bowl, beat sugar and butter together with an electric mixer, 2 minutes.
Add egg and beat for 1 minute more.
Mix in lemon juice and lemon zest. The mixture will look curdled, but will become smooth as it cooks.
Pour mixture into a 1-quart saucepan and cook over a medium low heat, whisking frequently, until curd is thick and curdled appearance disappears, 10-12 minutes. Do not let the curd boil.
Remove curd from the heat and transfer to a bowl or jar. Cover with plastic wrap and chill until cold, 1 hour.
Notes
Expert Tips
Whisk Constantly: This prevents the egg from curdling.
Low Heat: Cook the curd over low heat to ensure that it doesn't burn or turn grainy.
Strain the Curd: For a smoother curd, strain it to remove any bits of cooked egg or large pieces of zest.
Cool Completely: Let the curd cool before using it in any recipe, as it thickens further when cooled.