Preheat oven to 350 degrees F (175 degrees C). Grease or line muffin cups with paper liners.
Whisk carrots, eggs, milk, applesauce, canola oil, and vanilla extract together in a bowl. Mix flour, sugar, cocoa powder, baking soda, salt, and cinnamon together in a separate bowl; stir into carrot mixture until just combined into a batter. Fold chocolate chips and cranberries into batter. Spoon about 2 tablespoons batter into each prepared muffin cup.
Bake in the preheated oven until cupcakes are fluffy and a toothpick inserted in the center comes out clean, about 25 minutes.
