Preheat oven to 350° and place rack in the center of the oven.
In a large bowl, combine flour, granulated sugar, baking soda, baking powder, spices, cocoa, pepper, and salt. Whisk to combine, then stir in oil and eggs. Stir in carrots, apples, and pecans.
Set aluminum or paper cupcake holders in muffin tins. Spoon the batter into the cupcake paper cups, three-quarters of the way to the top. Bake approximately 20 minutes, or until a toothpick inserted in the middle comes out clean. Let cool completely before frosting.
Beat goat cheese, cream cheese, butter, and vanilla until smooth and fluffy, about 3 minutes. Gradually add powdered sugar and mix until combined.
Once cupcakes are cool, apply frosting.