In a heatproof bowl, rub the lemon zest into the sugar until fragrant. Whisk in the whole eggs and yolks until smooth.

In a small saucepan (Use a non-reactive saucepan, such as stainless steel or enameled, to avoid a metallic taste) combine the lemon juice and butter. Heat over low heat until the butter melts and the mixture reaches a very light simmer. Don’t heat the mixture up too quickly or it could cause the butter to separate.

Remove the saucepan from heat. Slowly whisk a few spoonfuls of the hot lemon mixture into the eggs to temper. Gradually add the rest, whisking constantly.

Return the mixture to the saucepan. Cook over medium heat, stirring constantly with a wooden spoon or spatula, until thickened (2–3 minutes). It should coat the back of the spoon.

Remove from heat and immediately strain through a fine-mesh sieve into a clean bowl. Whisk in salt and vanilla.

Press plastic wrap directly onto the surface to prevent a skin from forming. Cool to room temperature, then refrigerate for at least 1 hour before serving.