Whisk the coconut cream, oat milk, brown sugar, cornstarch, cinnamon, nutmeg, and sea salt in a saucepan until smooth.
Cook the base over medium heat for 5 to 7 minutes, whisking constantly, until lightly thickened. Stir in the vanilla extract and refrigerate the base for at least 4 hours.
Stir the grated carrots, flour, brown sugar, melted dairy free butter, oat milk, cinnamon, and baking powder together until a thick batter forms.
Spread the carrot cake batter in a thin layer on a lined baking sheet and bake at 350 F for 12 to 14 minutes. Cool completely, then cut it into small pieces.
Beat the dairy free cream cheese, powdered sugar, oat milk, and vanilla extract until smooth. Refrigerate the mixture until ready to use.
Churn the cold ice cream base in an ice cream maker until thick and creamy.
Layer the ice cream with carrot cake pieces and spoonfuls of cream cheese swirl in a freezer-safe container.
Drag a spoon through the layers to create ribbons, cover with parchment paper, and freeze for 4 hours.