Start by preheating your oven to 350 degrees, grease a loaf pan, and set aside.
Get a large liquid measuring cup, add 1 cup of vegan milk, and add 1 TB of vinegar, stir, and set aside.
Take a large mixing bowl and add the flour, sugar, baking soda, salt, and all the spices; whisk until combined well.
Add the remaining liquid ingredients, applesauce, vanilla, molasses, vegan butter, and oil, to the vegan milk/vinegar mixture and stir.
Add the liquid ingredients to the dry ingredients and stir until well combined, but don't over-mix. Pour this mixture into your prepared loaf pan and bake in the preheated oven for 50-55 minutes until a toothpick comes out mostly clean. This will continue cooking in its pan, so don't overbake it. Let it remain in the pan for about 10 minutes, then remove it to a cooling rack carefully to finish cooling.
Once the loaf is cooled, you can make the frosting. Take a small bowl and combine the frosting ingredients and stir with a fork until combined if it's too thin or too thick, add more powdered sugar or non-dairy milk. Now you can cover the loaf with the frosting, letting it drip down the sides.