Preheat your oven to 400 degrees. Line your muffin pan with muffin liners and set aside.
Mix together the flour, bran, baking soda, salt, cinnamon and nutmeg in a small bowl and set it aside.
In another bowl, mix together the melted butter, oil and sugar. To this add the egg, Greek yogurt, vanilla and mix until it is combined. From this point on, do not overmix.
Add the grated zucchini and mix it in as well. Last in is the dry ingredients. Mix this to combine. Scoop the batter into your lined muffin pan.
Move to the oven and bake for 7 minutes at 400 degrees. Reduce the heat and bake at 350 degrees for another 13-16 minutes.
Remove the pan from the oven and once it has cooled for a few minutes, gently take the muffins from the pan and let them cool on a cooling rack.
They can be eaten warm or cooled to room temperature.