Preheat oven to 350.
Tear bread slices into small, rustic pieces and place in a medium mixing bowl. Add grated carrots and toss to combine.
In another large bowl, whisk together eggs, milk, half and half, orange juice, melted butter, apple butter, vanilla, salt, and nutmeg.
Pour egg mixture over carrot and bread mixture and stir to combine.
Spoon bread pudding into greased muffin tins (12-count).
Bake at 350 for 45 minutes.
Remove from oven and allow cupcakes to cool slightly. Top with cream cheese frosting (plain or colored) and decorate with malted milk eggs, if desired.
*To make homemade Cream Cheese Frosting:
— Beat together 8 ounces softened cream cheese and 1/2 cup softened unsalted butter, until well combined.
— Add 3 cups confectioners’ sugar, 1 teaspoon pure vanilla extract, and 1/8 teaspoon salt, and beat until smooth and creamy.