Line the muffin pan with cupcake liners or spray with pan coating. Preheat an oven to 425°F. Line 12 standard muffin cups with paper liners. In a large bowl, stir together the flour, baking powder, baking soda, salt and cinnamon. In another bowl, whisk together the eggs and brown sugar until blended. Whisk in the buttermilk and butter. Add the egg mixture to the flour mixture and, using a rubber spatula, stir just until evenly moistened. Fold in the carrots just until evenly distributed.
Spoon the batter into the prepared muffin cups, filling them three-fourths full. Bake until the muffins are golden brown and a toothpick inserted into the center of a muffin comes out clean, 15 to 18 minutes. Transfer the pan to a wire rack and let cool for 2 minutes, then turn the muffins out onto the rack. Let cool briefly and serve.