Step 1: Preheat oven to 350 degrees F.
Step 2: Place paper liners in 18 muffin cups.
Step 3: In a large bowl whisk together the flour, sugar, baking soda, baking powder, salt, and ground cinnamon.
Step 4: Stir in the nuts and coconut. Set aside.
Step 5: In a separate bowl whisk together the eggs, oil, and vanilla extract.
Step 6: Fold the wet ingredients, along with the grated carrot and apple, into the flour mixture, stirring just until moistened.
Step 7: Evenly divide the batter between the prepared muffin cups and bake for 20 - 25 minutes or until a toothpick inserted in the center comes out clean.
Step 8: Remove from oven and let cool on a wire rack.
Step 9: After about 10 minutes remove the muffins from the pans and cool completely on a wire rack before frosting.
Step 10: Beat the butter and cream cheese until very smooth with no lumps.
Step 11: Gradually beat in the icing sugar until fully incorporated and smooth.
Step 12: Beat in the vanilla extract.
Step 13: Place a dollop of the cream cheese frosting on the top of each muffin.
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