Preheat the oven to 350 degrees Fahrenheit (177 degrees Celsius).
Make flaxseed eggs by mixing the 2 tablespoons of ground flaxseed meal with the 5 tablespoons of warm water in a small bowl. Then set the mixture aside for 7-10 minutes to firm up.
Prepare a 9x5 inch loaf pan by greasing it, dusting with flour, and then lining with parchment paper. The parchment paper is worth the extra step to ensure your bread doesn’t stick to the bottom.
Peel, core, and dice the apples. Set aside.
In a medium bowl, sift together the flour, cinnamon, nutmeg, baking soda, baking powder, and salt. Set aside.
In a large bowl beat the oil, flax eggs, sugar, and brown sugar with a whisk until well combined.
Add the vanilla, apple cider vinegar, and almond milk to the flax egg, oil and sugar mixture. Again beat to combine.
Slowly add the flour mixture a little at a time folding it in to combine well, but being careful not to overmix. The batter will be thick.
Fold in the diced apples and then pour the batter into the prepared loaf pan.
Bake at 350 degrees Fahrenheit (177 degrees Celsius) for 55 to 65 minutes until firm and golden brown. A cake tester should come out clean when the vegan apple bread is done.
Allow the bread to cool on a cooling rack in the pan for 20 minutes. Then turn out from the loaf pan and continue to cool in the cooling rack.