Preheat oven to 350º F and line a twelve ½-cup capacity muffin pan with paper liners.

In a medium size mixing bowl, combine the flour, baking soda, salt, cinnamon and nutmeg. Stir to distribute all ingredients.

In a large mixing bowl, combine the oil, brown sugar, eggs and vanilla and stir to blend together well.

With a wooden spoon, beat in about ¼ of the flour mixture with the wet mixture; repeat until all flour has been just combined with the wet ingredients. Don't over-mix or the cupcakes will be tough.

Stir in the carrots and coconut until just combined.

Fill the muffin cups two-thirds full with batter.

Bake on the middle rack of the oven for 18 - 22 minutes. Start testing with a toothpick at 18 minutes. When the toothpick comes out relatively clean, the muffins are done.

Let muffins cool in the pan for 5 minutes and then turn them out onto a rack to cool completely before frosting. You may have to use a thin, sharp knife to loosen the edges of the muffin tops a bit.

When the cupcakes are completely cool, combine the cream cheese, butter, molasses and powdered sugar in a bowl and beat until fluffy.

Spread icing on cupcakes with a butter knife or a small offset spatula.