In a large mixing bowl or stand mixer, beat the sugar, brown sugar, and coconut oil until creamed. Add the eggs and stir.
Slowly stir in the flour, cinnamon, sea salt, and baking powder until just combined. Do not overmix.
Fold in the vanilla extract and diced apples.
Pour the batter into a greased 13x9 baking dish. Bake for 35 minutes or until a toothpick inserted into the center of the cake comes out clean.
Remove the cake from the oven and allow to cool while preparing the frosting.
In a 1 quart saucepan, stir together the brown sugar, sugar, melted butter, cream and flour over medium heat until smooth. Pour over the cake and spread to cover the entire top of the cake. Allow to cool for at least 1 hour before serving.