Preheat oven to 350 degrees F.
In a small bowl, whisk together flours, baking powder, baking soda, cinnamon, pumpkin pie spice and salt; set aside.
In a separate bowl, whisk together eggs, pumpkin, maple syrup, cane sugar, applesauce, coconut oil, and vanilla until all combined. Add wet ingredients into flour mixture and mix with a spatula until just combined, being careful not to over-mix.
Pour pumpkin mixture into a prepared 9×5-inch loaf pan generously coated in oil or lined with parchment paper and bake in the oven for 50 to 60 minutes, or until a toothpick inserted in the center comes out clean.
Remove pumpkin bread from the oven and let it sit for 10 minutes, then remove it from the pan and let cool completely on a wire rack.
While the pumpkin bread is cooling, add cream cheese to a small bowl and heat in the microwave for about 30 seconds. Add in the maple syrup, a tablespoon of milk and 1/4 teaspoon of vanilla and whisk together until smooth. Feel free to add more milk a teaspoon at a time until you get a good consistency.
Drizzle the maple cream cheese glaze over top of the pumpkin bread, slice and enjoy!