Preheat oven to 400° F. Line 14 standard-size muffin cups with paper liners. Set aside.
In a large bowl, whisk together brown sugar, eggs, oil, butter and vanilla until completely combined.
In a separate bowl, whisk together flour, baking powder, baking soda, cinnamon and salt. Add the dry ingredients to the wet ingredients and stir just until combined (do not over-mix).
Fold in carrots, raisins, apples and pecans.
Divide batter evenly among prepared muffin cups, filling the muffin cups to the top. Sprinkle with coarse sugar, if desired.
Bake at 400° F for 10 minutes. Then, keep the muffins in the oven, but lower the oven temperature to 350 degrees F. Bake for an additional 10 minutes, or until a toothpick inserted in the center comes out clean. Let cool in the pan for about 5-10 minutes; transfer to a wire rack.