Preheat your oven to 375°F (190°C) and line a 12-cup muffin pan with paper liners. You can also grease the pan and dust it with flour.
In a large bowl, sift together the all purpose flour, sugar, baking powder, baking soda, salt, cinnamon, and nutmeg. Add the brown sugar and whisk until well combined.
In a separate bowl, mix together the oil, almond milk, apple cider vinegar, and vanilla extract.
Add the wet ingredients to the dry ingredients, stirring just until moistened. The batter should remain a little lumpy to prevent overmixing.
Fold in the shredded zucchini and chopped walnuts until evenly distributed.
Use an ice cream scoop or spoon to distribute the batter evenly among the muffin cups, filling each about three-quarters full.
Bake in the preheated oven for 20 to 22 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Allow the muffins to cool in the tin for a few minutes before transferring them to a wire rack to cool completely.
Store the muffins in an airtight container at room temperature for up to 3 days, or in the fridge for up to a week. You can also freeze them for up to 3 months.