Begin by zesting one large lemon using a microplane to create finely grated zest without the bitter white pith. Juice the remaining two lemons until you have about 2½ tablespoons of fresh lemon juice. Strain the juice through a fine-mesh sieve to remove any seeds and pulp.

In a small saucepan, combine 1 cup of heavy cream, ⅓ cup sugar, ¼ teaspoon kosher salt, and the lemon zest. Place the saucepan over medium-low heat, stirring occasionally, and allow it to simmer gently for about 5 minutes until the sugar dissolves and the cream is warm but not boiling.

Remove the saucepan from heat and whisk in the lemon juice and 1 teaspoon of vanilla extract until fully blended. Strain this mixture through the fine-mesh sieve into a clean bowl, discarding the lemon zest and any impurities for a smooth finish.

Take your lemon halves and gently scoop out the flesh, reserving it for another use if desired. Pour the creamy lemon mixture evenly into each lemon half, covering with plastic wrap and placing them in the refrigerator to chill for at least 4 hours.

When ready to serve, remove the lemon halves from the fridge and let them sit at room temperature for about 5-10 minutes to soften slightly before enjoying.