Preheat the oven to 350 degrees. Grease and flour a 9 inch cake pan.
Add the sugar, oil, water, non-dairy milk, and vinegar, and beat on medium speed until smooth.
Combine the arrowroot powder and non-dairy milk in a small container with a lid. Shake well and drizzle the mixture into the pan a little bit at a time, stirring constantly. The sauce should start to thicken.
Stir in the coconut and pecans, and heat through. If the sauce seems too sugary and thick, you may have to add a little bit more non-dairy milk. As it cools, it will thicken up.
Store leftover cake in an airtight container. It should stay fresh for up to 4 days.
You can make the sauce without nuts if you wish. Just add more coconut flakes.
If you aren't gluten free, go ahead and use regular all-purpose flour.