Preheat the oven to 350 degrees, and line a 12 cup muffin pan with cupcake liners.
In a food processor, cream together all the cheesecake swirl ingredients and beat them until they're whipped. Put the filling in a pastry bag with a large round tip, and set it into the refrigerator to chill.
In a mixing bowl of an electric mixer, cream together the butter, and sugar. Then add the eggs, coconut, walnuts and carrots and beat until combined.
Sift together the flour, baking powder, baking soda, salt, and all the spices. Stir them very gently into the batter. Do not overmix. Add the sour cream and vanilla and stir until just combined.
Divide the batter between the 12 muffin cups. Bake for 12 minutes.
Remove the pan from the oven, and pipe a cheesecake swirl into the top of each muffin. Actually press down into the muffin slightly.
Reduce the heat to 325 degrees and bake about 12 more minutes, or until a toothpick inserted into the carrot cake portion of the muffin comes out clean.
Cool in the pan for five minutes, and then on a wire rack for ten minutes.