Preheat oven to 375°F. Line a muffin pan with cupcake liners.
Grate carrots and apple; set aside.
Place oats into a blender or food processor and blend until they become a flour-like texture; add to a large bowl along with pastry flour, flaxseed, baking powder, baking soda, cinnamon, and nutmeg; mix well.
In a separate bowl, combine honey, applesauce, and egg. Stir wet ingredients into dry until just combined. Fold in carrots and apple.
Pour batter into muffin cups, and bake for 15-20 minutes or until a toothpick inserted into the center of a muffin comes out clean.