Sift the ingredients into a large bowl. Preheat the oven to 350F. Fill a baking dish with about a cup of water and place it on the bottom rack of the oven.
Add the pumpkin puree and coconut milk and mix to form a sturdy dough.
Whip the egg whites in a separate bowl. If needed, add some cream of tartar to the egg whites to help keep them stable.
Aggressively fold one-third of the egg whites into the dough to get it to absorb some of the moisture. Then, add the rest of the egg whites and gently fold them into the dough.
Grease a standard loaf pan. Spread the dough into the pan.