Step 1

Grate ½ tablespoon of zest from one lemon. Slice remaining lemons in half lengthwise, then with a spoon remove the entirety of the inside of the lemon and juice it through a fine-mesh sieve. Measure out 2½ tablespoons of lemon juice and save the rest of future use.

Step 2

In a small saucepan, bring heavy cream, sugar, salt, and lemon zest to a gentle simmer over medium-low heat. Continue to simmer, whisking occasionally for about 5 minutes. Whisk in lemon juice and vanilla extract, then strain mixture through a fine-mesh sieve.

Step 3

Evenly divide mixture into the lemon halves. Cover with plastic wrap and refrigerate for at least 4 hours. Let sit at room temperature for 5 to 10 minutes before serving.