Pour 1 cup whipping cream into a medium saucepan. Add 2/3 cup cake mix and whisk briskly over high heat until the well blended. Begin whisking again when bubbles form around the edges of the pan. Once the batter starts clumping together, immediately remove from heat and add the remaining 1 cup whipping cream. Whisk until it is smooth, and then pour into a 2 quart mixing bowl.
Break and separate 5 large eggs, pouring the egg yolks into a clean small mixing bowl. Clean and dry the saucepan used to heat the cake mix and whipping cream.
Pour 1 cup of whole milk into the clean saucepan. Add 2/3 cup sugar and whisk until all of the sugar is dissolved. Warm over medium heat, until bubbles form around the edge of the pan.
Pour about 1 cup of the warm milk mixture into the egg yokes and blend thoroughly, then pour back into the saucepan and continue heating over medium heat. Stir with a wooden spoon or rubber spatula until the mixture reaches 160 degrees (F).
Pour the custard base through a mesh strainer into the mixing bowl (from step 1) and whisk to combine the custard base and cake batter. Add ½ tsp of high-quality vanilla (I prefer Madagascar Bourbon). Cool over an ice bath until the mixture is cold to the touch, then refrigerate. After 5-12 hours of cooling, freeze according to the instructions that came with your ice cream maker.