Place a large clean glass bowl inside a larger bowl filled with ice. Place a fine mesh sieve over the clean bowl and set aside.
Combine the milk and cream in a heavy bottom medium saucepan. Heat on medium-low stirring frequently until bubbles start to form around the inside edges of the pan. If using an instant read thermometer, you are looking for a temperature of 170 degrees.
In a small mixing bowl whisk the egg yolks until smooth. Gradually whisk in the granulated sugar and continue whisking until the mixture is pale and thick.
Slowly temper the egg yolks by adding a drizzle of the hot milk mixture while whisking constantly. Continue whisking and adding the hot milk until all ingredients are combined.
Return the custard to the saucepan and heat on medium-low stirring constantly with a wooden spoon. Cook until the mixture reaches 185 degrees or when the custard coats the back of the wooden spoon. Do not boil the custard.
Pour the custard through the sieve into the bowl in the ice water bath. Allow the custard to cool for about 30 minutes. Stir every 5 minutes or so then when cooled, cover and refrigerate overnight or for at least 4 hours.
When ready to make the gelato stir in the key lime juice and zest. Process according to the manufacturer instructions.
If making ice cream sandwiches, pour the gelato into a plastic wrap lined flat casserole dish with a 2" side. Depending on the desired thickness, you can use a 13x9" pan or smaller. Cover with plastic wrap pressed on the top of the gelato and freeze until solid. Overnight works best.
Once frozen, remove the gelato using the plastic wrap and place on a cutting board. Using the desired cookie cutter, cut out the gelato and place between two graham crackers. Freeze in an airtight container until ready to serve. Remove the ice cream sandwiches 10 minutes before serving.