Set a fine-mesh strainer over a clean bowl. Prepare an ice bath if chilling quickly.
Whisk sugar and egg yolks in a medium saucepan until smooth and slightly lightened.
Stir in lemon zest, lemon juice, and salt until fully combined.
Cook over medium-low heat, stirring constantly, until thickened and 170–175°F, about 8–10 minutes.
Strain the curd through the prepared strainer to remove zest and any lumps.
Whisk in butter pieces until melted and glossy. Add vanilla, if using.
Press plastic wrap directly onto the surface. Chill until set, at least 2 hours.
Stir before serving. Keep refrigerated and use clean utensils to scoop.