In a blender, blend together the heavy cream and 1 cup peach cobbler filling, without crumbles. (Just scrape the crumbles off the top and use the filling for this step.) Set aside.
In a large bowl, whisk together the milk and sugar 'til the sugar dissolves, about 1-2 minutes.
Whisk the blended cream/cobbler mixture, vanilla extract, sea salt, and cinnamon 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 up peach cobbler.
Turn off the machine and scoop the soft-serve ice cream into airtight containers; place in the freezer for 3-4 hours, or overnight, to firm up more. Serve when ready.