Make an ice bath set up by placing a strainer over a medium bowl and setting this bowl in a larger bowl containing ice water. You just need a cup or two of ice in enough water to just barely float the ice. Have this near your stove to quickly strain and cool the custard mixture. Pour 1 cup of the heavy cream into the medium bowl of your ice bath (this will help cool the custard quicker when it is poured in to the cold cream)

Heat the milk, the remaining 1/2 cup of the cream, and sugar in a medium saucepan over medium heat, stirring occasionally to dissolve sugar, until steam appears and the milk is warm (about 175 degrees), about 5 minutes.

While milk mixture is heating, whisk the egg yolks in a large glass measuring cup or a bowl until smooth and pale yellow, about 30 seconds. Slowly add half the warm milk mixture into the beaten yolks while whisking quickly- you don't want scrambled eggs. Whisk this milk and egg yolk mixture back into the warm milk in the saucepan; place the saucepan over medium heat and cook, stirring constantly with a wooden spoon or heat proof spatula, until steam appears, foam subsides, and the mixture is slightly thickened (an instant-read thermometer will read about 180 degrees) The mixture will coat the back of the spoon and if you run your finger across the coating it will leave a trail that stays. Be careful not to boil the mixture as the eggs will curdle.

Immediately pour the custard through the strainer into the bowl set in the ice bath. Allow to cool to room temperature, stirring it occasionally . Stir in vanilla extract. Cover and refrigerate at least 8 hours or overnight.

Mix together the graham cracker crumbs and sugar. Add in melted butter and mix with a fork until crumbs are uniformly coated. Press into a pie plate and bake in a preheated 350 degree oven until lightly browned and fragrant, about 10 to 13 minutes. Allow to cool completely then break up into crumbs and pieces. Set aside.

Beat together softened cream cheese, lemon zest and lemon juice until smooth and combined. Gradually beat in cooled custard mixture and mix until uniform and combined.

Freeze in ice cream maker according to manufacturer's instructions.

Layer in container with graham cracker crumbs. I like to do 2 or 3 layers of graham cracker crumbs between layers of ice cream (you most likely will not use all the crumbs). You could also reserve the crumbs and use as topping instead.

Freeze the ice cream a couple of hours or until firm. If it gets too firm, allow to sit at room temperature for about 10 minutes before serving.