Preheat your oven to 350°F (175°C) and line a muffin tin with paper liners or grease it lightly.
In a large bowl, combine the rolled oats, grated zucchini, grated carrot, all-purpose flour, brown sugar, baking powder, baking soda, ground cinnamon, and salt. Mix well.
In a separate bowl, whisk together the honey (or maple syrup), vegetable oil, milk, eggs, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and stir until just combined. If desired, fold in the chopped nuts or chocolate chips.
Divide the batter evenly among the muffin cups, filling each about 2/3 full.
Bake for 18-20 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Allow the muffins to cool in the pan for 5 minutes before transferring them to a wire rack to cool completely.