Step 1

Make the cupcakes: Preheat the oven to 350 degrees F. Line a 12-cup muffin pan with paper liners. Whisk the flour, baking soda, cinnamon, cloves and salt in a medium bowl. Put the cocoa powder in a large bowl. Warm the milk in a small saucepan or in the microwave until just about to simmer. Pour the milk over the cocoa powder and whisk until smooth. Whisk in the granulated sugar, vegetable oil, egg and vanilla. Whisk in the flour mixture until just combined.

Step 2

Divide the batter among the prepared muffin cups, filling each three-quarters of the way. Bake until a toothpick inserted into the centers comes out clean, 20 to 25 minutes. Transfer to a rack and let cool 10 minutes in the pan, then remove the cupcakes to the rack to cool completely.

Step 3

Meanwhile, make the frosting: Microwave the chocolate in a small microwave-safe bowl in 30-second intervals, stirring, until smooth; let cool slightly. Beat the butter in a large bowl with a mixer on high speed until light and fluffy, about 2 minutes. Reduce the speed to low; add the confectioners' sugar and salt and beat until combined, then increase the speed to high and beat until creamy, about 3 more minutes. Reduce the speed to medium; add the heavy cream and vanilla and beat until fluffy, about 1 minute.

Step 4

Remove about one-third of the frosting to a small bowl and stir in the melted chocolate and cocoa powder until smooth; set aside. Tint the remaining frosting bright orange with food coloring. Transfer the orange frosting to a piping bag fitted with a large round tip.

Step 5

Cut a small cone-shaped chunk out of the center of each cupcake with a paring knife, cutting about halfway into the cupcake. Crumble the chunks of cake into a bowl. Spread the chocolate frosting in a thin layer on the cupcakes, leaving the carved-out holes open. Pat the cupcake crumbs on the chocolate frosting to look like dirt. Pipe the orange frosting into each hole, mounding it above the surface to look a like carrot. Stick a few sour apple laces into the orange frosting to look like carrot tops.