Zest one fresh lemon, being careful to avoid the bitter white pith. Squeeze all the lemons through a fine-mesh sieve to extract their juice.

In a small saucepan, blend together the heavy cream, sugar, salt, and lemon zest. Warm the mixture gently over medium-low heat for about 5 minutes.

Remove the saucepan from heat and stir in the freshly squeezed lemon juice and vanilla extract.

Strain the mixture through a fine-mesh sieve into a clean bowl or jug.

Carefully pour the strained mixture into prepared lemon halves.

Cover the filled lemon halves with plastic wrap and place them in the refrigerator for at least 4 hours.

Before serving, let the Lemon Pudding sit at room temperature for 5 to 10 minutes.