In a large saucepan, combine the heavy cream, half and half, salt, sugar, and lemon zest. Over medium-low heat, stirring very frequently, heat the mixture until bubbles form around the edges. Remove from heat.

While the mixture is heating, whisk 5 egg yolks together. After you’ve removed the cream mixture from heat, remove 1 cup of the hot cream mixture from the pan. Very slowly, just a few tablespoons at a time, and whisking constantly, pour the hot cream mixture into the eggs. If you add the cream mixture too quickly the eggs will scramble, so go slow and be patient.

After you’ve added all the hot cream mixture, return the pan with the cream mixture to medium-low heat and slowly whisk in the egg mixture. Heat, stirring constantly, until thickened–it’s ready when you dip the back of a spoon into the mixture and, when you drag your finger through it, it leaves a trail. Remove from heat and Ccill in the refrigerator (for several hours or overnight).

When the mixture is chilled, add the freshly squeezed lemon juice, stir to combine, and freeze according to your ice cream maker’s instructions (a 4-5 quart machine). While the ice cream is churning, take a package of shortbread cookies and break them. During the final few minutes of churning (or after you remove the ice cream from the machine), mix in the broken cookies. Transfer to a freezer-safe container and freeze for at least four hours before serving. Makes 10-12 servings.