Preheat the oven to 350°F (175°C) and line a muffin tin with paper liners or lightly grease it.
In a large mixing bowl, whisk together the applesauce, plant-based milk, apple cider vinegar, brown sugar, oil, and vanilla extract until smooth and well combined.
In a separate bowl, whisk together the all-purpose flour, baking powder, cinnamon, nutmeg, and salt until well combined. Gradually add the dry ingredients to the wet ingredients, stirring until just combined.
Fold in the diced apple and chopped nuts, if using.
Divide the batter evenly among the prepared muffin cups, filling each one slightly more than three-quarters full. Top each muffin with additional diced apple and sprinkle with brown sugar.
Bake in the preheated oven for 24-26 minutes, or until a toothpick inserted into the center of a muffin comes out clean. Remove from the oven and let the muffins cool in the muffin tray for a few minutes before transferring them to a wire rack to cool completely.