Preheat the oven to 375 degrees. Grease a round 9-inch cake pan or springform pan.
Prepare the topping by placing the maple syrup, cinnamon, cranberries, apples, apple cider, and arrowroot starch in a medium saucepan. Cover and bring to a boil, then lower the heat to a simmer. Simmer uncovered over low heat for 10 minutes, stirring occasionally, to thicken the mixture (or until the cranberries have burst and the apples have softened). Mash the mixture with a potato masher or a fork. Set aside to cool.
In the large bowl of an electric mixer, combine the eggs, coconut oil, maple syrup, and vanilla extract on low speed.
Add half the flour mixture to the wet ingredients, then add half the milk. Repeat with the remaining flour mixture and milk. Mix on medium high speed until the flour mixture and milk are fully incorporated, then transfer the batter to the prepared pan.
Spread the cooled fruit mixture evenly over the batter without stirring it into the batter.
Bake for about 45 minutes, or until a toothpick inserted in the middle of the cake comes out clean. Don't let the cake bake for too long, or it will be dry. Let the cake cool to room temperature before cutting.