In a stand mixer with a whisk attachment, whip heavy cream until stiff peaks form, whisking in the vanilla extract and corn syrup, the last 20 seconds.
With a rubber spatula, gently fold in the condensed milk. The mixture will deflate some and look slightly looser, but be gentle. Gently fold in the mini chocolate chips.
Into a 9×5 loaf pan, or 9×9 square baking dish, spread out 1/3 of the ice cream mixture. Dollop a few spoonfuls of the strawberry jam over the top, and run a knife through the mixture to create a strawberry swirl. Drizzle with 1/3 of the chocolate magic shell. Repeat this for the next two layers. Top the ice cream with extra chocolate chips or strawberry jam, or fresh chopped strawberries if desired. Freeze at least 4 hours, 6 or overnight is preferred.