Preheat oven and prep muffin pan: Preheat oven to 350 degrees Fahrenheit (about 175 degrees Celsius). Then either place muffin liners (either paper or silicone) into a 12-count muffin pan or grease the muffin tins with vegan butter or a light oil, like avocado oil.
Optional: vegan butter or oil to grease pan
Make flax egg: Combine the 2 tablespoons ground flax seeds with ¼ cup hot water in a small bowl and let sit 5 minutes to make a flax egg replacer.
2 tablespoons ground flax seeds, ¼ cup hot water
Mix dry ingredients: In a large mixing bowl, add 1 ½ cups whole wheat flour, 1 cup wheat bran, ½ cup light brown sugar, 1 teaspoon baking soda, and ½ teaspoon salt. Whisk together to combine.
1 ½ cups whole wheat flour, 1 cup wheat bran, ½ cup light brown sugar, 1 teaspoon baking soda, ½ teaspoon salt
Mix wet ingredients: In a medium bowl, add 1 ¼ cups plant-based milk, ½ cup apple sauce, 1 tablespoon apple cider vinegar, 1 tablespoon vanilla extract, and the thickened flax egg. Whisk together to mix well.
1 ¼ cups plant-based milk, ½ cup apple sauce, 1 tablespoon apple cider vinegar, 1 tablespoon vanilla extract
Combine wet and dry ingredients: Add the mixed wet ingredients to the dry ingredients and use a baking spatula or scraper to fold in the wet ingredients until they are well combined and all of the flour is wet, but do not over mix.
Add to muffin pan and bake: Add 1/4 cup mixed bran muffin batter to each muffin tin, then bake in the preheated oven for 15-20 minutes, or until you can stick a toothpick in and it comes out clean. Then remove the muffins from the tin and let cool on a baking rack at least 10 minutes before serving.