In a medium saucepan, combine milk and cream and heat over medium-low heat until small bubbles start to form around the outer edge of the pan, stirring occasionally. While the milk and cream are heating, whisk together egg yolks and then add in sugar, continue to beat until pale yellow.
When the milk and cream have reached 170º F temper the egg yolks by adding a cup or two of the hot cream to them and slowly while constantly whisking. Add the mixture to the pan, pouring slowly and whisking. Heat over low heat, stirring frequently, until the mixture is thick enough to cover the back of a wooden spoon and reaches 185º F, without allowing it to boil.
Strain the mixture through a mesh strainer to remove any possible lumps. Slowly add in lime juice, vanilla extract and lime zest. Cool slowly to room temperature, stirring every so often, and then cover and refrigerate until cold.
Once the gelato mix is cold, freeze it in an ice cream maker according to manufacturer's directions. Stir in frozen graham cracker crumbs and transfer immediately to an airtight container. Freeze until firm and serve.