In a blender, blend together the heavy whipping cream and 1 cup of gooey butter cake. Set aside.
In a large mixing bowl, whisk together the milk and sugar 'til the sugar dissolves, about 1-2 minutes.
Whisk the blended cream and cake mixture, vanilla extract, and sea salt into the milk mixture.
Turn on the ice cream maker, and pour the mixture into the pre-frozen freezer bowl* with the churn paddle in place.
Place the cover on top, and freeze the ice cream 'til it thickens, about 20-25 minutes.
In the last 2-3 minutes of freezing, slowly add 1 cup of cold diced gooey butter cake.
When the ice cream has a soft, creamy texture, turn off the machine, and scoop the soft-serve ice cream into an airtight container, and place it in the freezer for 3-4 hours, or overnight, to firm up more. Then serve when ready.