Combine whole wheat pastry flour, oat flour, and next 6 ingredients (through salt) in a medium bowl, stirring with a whisk.
Whisk carrots, Greek yogurt, and next 5 ingredients (through vanilla extract) in a separate bowl until combined.
Add carrot mixture to flour mixture and stir just until moist. Gently fold in cooked rice.
Place 20 paper muffin cup liners in muffin cups; coat liners with cooking spray. Spoon batter into prepared cups, until 2/3 full. Bake at 350° for 20 to 25 minutes or until a wooden pick inserted in center comes out clean. Cool 10 minutes in pan on a wire rack; remove from pan.
Store muffins in the refrigerator or freezer to keep fresh.