Preheat the oven to 350 degrees and grease a 12 cup bundt pan.
In a small bowl, mix the flour, baking powder, cinnamon, baking soda, and salt.
In a large bowl, beat the eggs. Then add the maple syrup, coconut oil, and vanilla extract. Stir together, and add the dry ingredients to the large bowl. Stir in the apples.
Transfer the batter to the pan and bake for 50 to 55 minutes, or until a toothpick inserted in the cake comes out clean.
Cool the cake in the pan for 10 minutes, then remove it from the pan and cool completely on a wire rack.
To make the glaze, stir together the coconut milk and maple syrup in a small pot. Bring to a gentle simmer. In a small bowl, stir together the arrowroot powder and vanilla extract. Add this mixture to the small pot and whisk to thicken for a couple minutes. Use a large spoon to drizzle the glaze all along the top of the cooled cake.