Preheat oven to 350 degrees F. Line a standard muffin pan with cupcake liners and set aside.
In the cup of a kitchen blender, blend carrots, oil, melted butter, 1 tbsp vanilla, salt, eggs, flour, and baking powder until well combined. Make sure to run a spatula along the sides to mix flour well. If necessary, blend a little more until mixture is homogeneous.
Pour mixture into cupcake liners, filling 3/4 full. Bake for about 18-20 minutes or until toothpick inserted in the center comes our clean. While they are cooling down, prepare cream cheese frosting.
In the bowl of a mixer, combine softened cream cheese and butter, powdered sugar, and 1 tbsp vanilla. Beat until homogeneous, creamy, and smooth (without lumps).
Place frosting into a piping bag and reserve. Once carrot cupcakes are cool, make a hole in the center using a melon ball or teaspoon. Fill each with 1 tsp Nutella. Then, top cupcakes with cream cheese frosting and garnish with Cadbury eggs, or as desired.
Store leftovers in a clean airtight container in the fridge for up to 3 days. You can freeze carrot cupcakes (without the filling and topping) in a freezer bag for up to 6 months.