Preheat oven to 400°F. Coat a 12-cup muffin tin with cooking spray.
In a large bowl, toss carrots, walnuts and pineapple with 2 Tbsp. flour.
In a separate large bowl, combine remaining all-purpose flour, whole-wheat flour, baking powder, baking soda, salt, cinnamon and oats. In a medium bowl, whisk together buttermilk, oil, brown sugar and egg, breaking up any clumps of sugar. Add buttermilk mixture to flour mixture and stir until just moistened. Stir in carrot mixture until just combined.
Divide batter among muffin cups and bake until a toothpick inserted into center of a muffin comes out clean, 20 to 25 minutes. Let cool on a wire rack for 5 minutes, then turn muffins out of pan onto rack to cool.