Grate ½ tablespoon of zest from one lemon and set aside.
Slice all lemons in half lengthwise. Use a spoon to scoop out the inside flesh and juice completely. Strain the juice through a fine-mesh sieve and measure out exactly 2½ tablespoons. Reserve the remaining juice for another use. Set the cleaned lemon shells aside.
In a small saucepan over medium-low heat, combine the heavy cream, sugar, kosher salt, and lemon zest. Bring to a gentle simmer. Continue to simmer, whisking occasionally, for about 5 minutes until slightly thickened.
Whisk in the lemon juice and vanilla extract. Remove from heat.
Strain the entire mixture through a fine-mesh sieve into a bowl or pourable measuring cup.
Evenly divide the warm mixture into the hollowed-out lemon halves. To keep them upright, nestle them into a muffin tin.
Cover loosely with plastic wrap and refrigerate for at least 4 hours, or overnight, until fully set.
Remove from the fridge 5 to 10 minutes before serving to soften slightly. Serve as-is or topped with fresh berries, a dusting of powdered sugar, or a curl of lemon zest.
