Preheat your oven to 375 degrees, grease an 8x8 glass dish, and set it aside.

Make your flax egg by combining 3 TB flax meal with 6 TBs water, stir and set aside.

Take a large bowl and combine the non-dairy milk, brown sugar, white sugar, melted vegan butter, cinnamon, and vanilla; whisk until combined well. When the flax egg has gelled for about 5 minutes, add it to this mixture and whisk.

Cut your bread into cubes, then add the cubes to the liquid mixture and stir until combined. Pour this into the prepared pan and bake uncovered for 30 minutes. After 30 minutes, cover the bread pudding with foil and bake for an additional 20 minutes. Remove from the oven, remove the foil, and let sit while making the vanilla sauce.

To make the vanilla sauce, get a small saucepan, add the non-dairy milk and flour, mix until well combined, then add the sugar, vegan butter, and cinnamon, and stir. Let this cook on high until it starts to boil, stirring frequently, so it doesn't burn. When it comes to a boil, turn it down to medium and stir while it boils lightly for a few minutes; it should coat the back of a spoon. Remove from heat.

Cut your slices and then pour the vanilla sauce on each slice to serve.