Preheat the oven to 350 degrees F. Line a half sheet pan with parchment paper and grease with 2 teaspoons of the butter.
In the bowl of an electric mixer, fitted with a paddle, combine the 1/2 cup butter, oil and sugar. Cream the mixture until smooth.
Sift the flour, baking powder, baking soda, cinnamon, and salt into a small mixing bowl. Add the egg to the butter/sugar mixture, one at a time. Add the flour mixture to the butter/sugar mixture, 1/2 cup at a time. Add the carrots and pineapple. Mix well. Pour the batter into the prepared pan and spread evenly. Place in the oven and bake for about 25 to 30 minutes or until the center sprigs back when touched.
Remove from the oven and cool. Using a 2 1/2-inch round cookie cutter, cut the cake into 24 rounds.
In the bowl of an electric mixer, combine the cream cheese and remaining 1/2 cup butter. Mix well. Add the coconut. Mix well. Add the powdered sugar, 1 cup at a time and mix until the frosting is spreadable. Spread 2 tablespoons of the frosting in the center of half of the cake rounds. Place the remaining cake rounds on top of the frosting. Frost each round with the remaining frosting. Garnish the top of each cake with a sprinkle of the chopped macadamia nuts.