Preheat the oven to 350 degrees F and grease a standard loaf pan (9x5 inches). I also like to line the pan with parchment paper for easy removal after baking.
In a large bowl, combine the soy milk and ground flaxseeds. Stir, then let sit for 2 minutes to thicken a bit. Now add the sugar, melted vegan butter and vanilla and whisk until well combined.
Add the flour on top of the wet ingredients, then the baking powder and salt. Use a wooden spoon or spatula and mix until just combined. Do not over mix or the bread will be dense.
Pour half of the batter into the prepared pan, reserving the other half in the bowl.
In a small bowl, combine the brown sugar and cinnamon. Set aside.
In a medium sized bowl, combine the apple filling ingredients. Spoon half of the apples on top of the batter in the pan.
Pour the rest of the batter on top of the apples, then top with the remaining apples. Push the apples down into the batter a bit with your hands.
Sprinkle the brown sugar cinnamon on top of the apples.
Place the bread in the oven with a pan in the rack below in case any apple juices drip. Bake for 1 hour and 15 minutes or a little longer, until a toothpick inserted in the middle comes out mostly clean.
Let cool in the pan for 30 minutes, then transfer to a cooling rack.
In a small bowl (optional), stir the powdered sugar and milk together to form the glaze. Drizzle over the top of the bread. Slice, serve immediately and enjoy!