In a large bowl, mix the flour, baking soda, baking powder, spices and salt.
In a smaller bowl, whisk together the applesauce, oil, sugar, vanilla extract, sweet potato and non-dairy milk until well mixed.
Add the wet ingredients to the dry ingredients and mix just until you have a smooth batter.
Grease a 9-inch square cake pan or, for easier removal, line the bottom of the pan with parchment or foil and oil the surface.
Pour the batter into the pan and with a spatula or ladle spread evenly and smooth out the top.
Preheat the oven to 350 degrees Fahrenheit. Bake in the oven 25 minutes or until a toothpick inserted in the center comes out clean.
Make the glaze by whisking together the peanut butter, water, vanilla and powdered sugar until you have a smooth mixture.
Let the muffin "cake" cool for 10 minutes. Unmold the cake, place on a rack, then pour the glaze over with a spoon, ensuring you spread it evenly.
Cool thoroughly before serving.