How to Make It
Preheat the oven to 350º. Puree the apple and carrots in a food processor and set aside. Line a 6-muffin tin with large paper cups, and set aside.
In a large bowl, mix the flour, flax seed meal, sugar, baking soda, baking powder, salt, and cinnamon. In a separate bowl, combine the milk, eggs, and vanilla. Mix well, and slowly pour the liquid ingredients into the dry ingredients, stirring. When the wet and dry ingredients are combined, add the apple and carrot puree. Gently stir to combine without overmixing.
Using a measuring cup or scoop, evenly divide the batter between the muffin cups. (They will fill nearly all the way to the top, and because these are gluten-free muffins, they aren't going to rise too much.) Sprinkle the flax seeds on top of each muffin. Bake, uncovered, for 20-30 minutes or until a toothpick inserted in the center of the muffin comes out clean. Cool in the muffin tin for 5 to 10 minutes.
Because store-bought flax seed meal lacks the nutritional value of whole flax seeds, it's best to make a fresh, coarse-ground flax seed meal just before you use it. Flax seed meal is easy to make with a with a food processor, clean coffee grinder, or blender. One cup of whole flax seeds yields about 1 2/3 cups of flax seed meal, so leave room for expansion (use any leftover flax seed meal in smoothies or sprinkled on top of cereal or yogurt).