Zest one lemon to capture its fragrant oils, then juice all the lemons.

Combine heavy cream, sugar, salt, and lemon zest in a saucepan and simmer for 5 minutes.

Remove from heat, stir in lemon juice and vanilla extract, then strain to eliminate lumps.

Pour the mixture into prepared lemon halves.

Cover with plastic wrap and chill for at least 4 hours.

Let sit at room temperature for 5 to 10 minutes before serving.