Preheat the oven to 400 degrees. Line 2, 12-count pans with cupcake liners. You can also butter them if you don't want to use liners. Set these aside.
Mix together the flour, sugar, baking powder, baking soda, salt, cinnamon, and nutmeg in a small bowl and set this aside.
In another medium-size bowl, mix together the oil, melted butter, eggs, yogurt, and vanilla.
Combine the wet and the dry ingredients, only mixing to combine. Last are the carrots and nuts if you are using them. Again, only mix to combine.
Spoon them into your muffin pans. It should fill up each cavity about ¾ of the way.
Bake for 5 minutes at 400 degrees. Then, reduce the temperature to 375 degrees and bake for another 11-14 minutes. Be sure not to overbake! This will dry out the muffins.
Remove them from the oven and let them cool in the pan for 3-5 minutes, then gently remove them from the pan and let them cool on a cooling rack.