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Preheat oven to 350ºF.
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Using a blender or food processor, grind 2 1/2 cups of old fashioned oats into oat flour. You may need to do this in batches - I use a regular blender and do 1 cup at a time. You can also use 2 1/4 cups plus 2 Tbsp. pre-ground oat flour.
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In large bowl, mix all ingredients except apple and carrots until combined. Fold in apple and carrots.
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Scoop muffin batter into greased muffin pans, filling almost to the top of the pan. Bake for 20-22 minutes. Cool completely before removing muffins from pans.