Preheat oven to 350. Spray 2 miffins tin pans and set aside.
Shred enough carrots to make 2 cups, about 3 large carrots.
Mix oil, eggs, and sugar in a bowl. Add flour, baking powder, and salt. Mix well.
Add banans and vanilla and use an electric mixer to mix well, mashing the bananas as you go. (if you don't have an elelctric mixer, you will need to mash the bananas first.)
Add carrots and stir. Spoon into muffin tins, filling each one about 2/3 full.
Bake at 350 for 13-15 minutes. (longer for large muffins, less for mini-muffins)
Notes
You may use leftover, ground up carrots instead of shredded carrots. You may also use baby food carrots, but if you do - use only 1 cup puree.