1. Prepare your baking pan and oven: Preheat your oven to 350 F (175 C). Lightly grease and flour a 9×5-inch loaf pan, or line it with parchment paper, leaving an overhang on the sides for easy removal. This prevents sticking and makes cleanup a breeze.

2. Combine the dry ingredients: In a large mixing bowl, whisk together the all-purpose flour, rolled oats, granulated sugar, brown sugar, baking soda, ground cinnamon, and salt. Make sure there are no lumps and everything is evenly distributed.

3. Mix the wet ingredients: In a separate medium bowl, whisk together the unsweetened applesauce, dairy-free milk, vegetable oil, large egg, and vanilla extract until well combined and smooth.

4. Combine wet and dry mixtures: Pour the wet ingredient mixture into the dry ingredient mixture. Stir with a spatula or wooden spoon just until everything is moistened and no dry streaks of flour remain. Be careful not to overmix, as this can lead to a tough bread. A few small lumps are perfectly fine.

5. Transfer to the loaf pan: Pour the batter evenly into the prepared loaf pan. You can gently tap the pan on the counter a few times to settle the batter and remove any large air bubbles.

6. Bake until golden: Place the loaf pan in the preheated oven and bake for 45-50 minutes, or until a wooden skewer or toothpick inserted into the center of the loaf comes out clean. The top should be golden brown and spring back when lightly touched.

7. Cool before slicing: Once baked, remove the loaf pan from the oven and let the bread cool in the pan for about 10-15 minutes. Then, carefully lift the bread out of the pan using the parchment paper overhangs (if used) or invert it onto a wire rack to cool completely before slicing. This allows the bread to firm up and prevents it from crumbling.