Add 2 cups heavy cream, ¾ cup granulated sugar, and 1 tablespoon lemon zest to a medium saucepan and heat over medium heat until the sugar dissolves and the cream is steaming, stirring constantly.
Reduce the heat to medium-low and let the cream mixture simmer for 2 minutes before adding 6 tablespoons fresh lemon juice and 1 teaspoon vanilla extract. Stir to combine and continue to cook for 1-2 minutes, until it begins to thicken.
Remove from the heat and press through a fine mesh strainer to remove the zest and any pulp.
Pour the mixture into 4 4-ounce ramekins or dessert cups. Cover and chill for 3 hours, or overnight.
Serve with a dollop of whipped cream and fresh berries, if desired.