Position rack in center of oven and preheat the oven to 350 degrees F. If not using muffin cups then grease the wells of the muffin pan with the butter and set aside.
Sift the flour, sugar, baking soda, cinnamon, and salt into a mixing bowl. Stir in the carrots, parsnips, raisins, pecans, coconut, and apple.
In another bowl, combine the eggs, vegetable oil, and vanilla extract and whisk until smooth.
Add the wet mixture to the flour mixture and stir until the batter is just blended.
Spoon equal amounts of the batter into the wells.
Bake until the muffins spring back to the touch and are golden brown, about 35 minutes.
Using oven mitts or pot holders, carefully remove the muffins from the oven and transfer to a wire rack to cool for 5 minutes.
Remove the muffins from the muffin pan and set aside to cool completely.
Recipe courtesy of Emeril's There's A Chef In My Family, by Emeril Lagasse, Harper Collins Publishers, 2004