In a medium saucepan, whisk together the brown sugar, cornstarch, cinnamon, and salt. Whisk in the coconut milk, molasses, and corn syrup, then cook over medium heat, whisking constantly, for 5 to 7 minutes, until the base simmers and thickens slightly.
Remove from the heat and stir in the vanilla. Pour into a bowl, press plastic wrap onto the surface, and refrigerate for at least 6 hours or overnight.
Preheat the oven to 350°F and line a baking sheet with parchment paper. In a bowl, mix the oats, flour, brown sugar, cinnamon, baking soda, and salt, then stir in the melted butter and vanilla until clumpy.
Scatter the mixture over the baking sheet in small clumps and bake for 12 to 15 minutes, until deep golden brown. Let it cool completely on the sheet, where it will crisp up, then break into bite-size pieces.
Pour the chilled base into an ice cream maker bowl that has been frozen for at least 24 hours. Churn for 20 to 25 minutes, until thick and creamy like soft serve.
Microwave the marshmallow creme for 10 seconds to loosen it. Layer the ice cream into a 9x5-inch loaf pan with handfuls of oatmeal crumble and spoonfuls of marshmallow creme, then gently swirl with a skewer.
Cover tightly and freeze for 4 to 6 hours, until firm. Let sit at room temperature for 10 minutes before scooping.