Combine the sugar, lemon zest and eggs in a saucepan over medium heat, stirring with a whisk. Cook until sugar dissolves and the mixture turns light in color (about 2-3 minutes).
Stir in lemon juice and cook for about 5 minutes or until mixture thinly coats the back of a spoon, stirring constantly with a whisk.
Remove from the heat and whisk in the cold butter and vanilla bean paste or extract.
Strain the curd for a smoother texture.
Cool the lemon curd before covering and chilling in the fridge for at least 2 hours.