In a saucepan whisk together the zest, the lemon juice, the sugar, and the eggs, whisk in 1 cup of the half-and-half and the vanilla, and cook the mixture over moderately high heat, whisking constantly, until it just comes to a simmer.

Strain the custard through a fine sieve into a bowl, pressing hard on the zest, and chill it, covered with plastic wrap, until it is cold.

Whisk in the remaining 1 cup half-and-half and freeze the mixture in an ice-cream freezer according to the manufacturer’s instructions. Makes about 1 quart.