Preheat oven to 325° F. In a medium saucepan, combine cream, lemon zest, and salt. Warm mixture over medium-low heat until steam just begins to rise from the surface. Remove from heat and let the mixture sit for 15 minutes.
In a small bowl, whisk yolks and sugar together until well combined. Add a splash of the the cream into the egg-sugar mixture, then pour the mixture into the saucepan of cream. Add vanilla extract and stir to combine.
Strain the warm mixture into a 1-quart heatproof measuring cup with a spout. Pouring carefully, divide the mixture between six 6-ounce ramekins.
Set the ramekins in a baking dish and place it in the preheated oven. Carefully add boiling water to the pan so it reaches halfway up the sides of the ramekins, taking care not to splash water into the ramekins (if you use a 9 by 13-inch glass pan with 6-ounce ramekins, you’ll need about 4 cups boiling water).
Bake until centers are barely set (they should still wobble when you nudge the pan), about 35 to 40 minutes. Remove the baking pan from the oven and let the ramekins cool in the water bath until you can remove them without burning your fingers.
Transfer the ramekins, uncovered, to the refrigerator. Chill until cold, at least 3 hours. .