Carrot Cupcakes:
Preheat the oven to 375 F (190 C).
Line a muffin tin with paper liners.
In a bowl, mix the butter, oil, and sugar without overmixing.
Add the eggs and vanilla, still without overmixing.

Sift the dry ingredients, then add them to the previous mixture. Beat the dough well, then incorporate the grated carrots.
Fill the molds to 1/4″ (0.5 cm) from the edge and bake for 25-30 minutes.

Cream Cheese Frosting:
Using an electric mixer, cream the cream cheese and butter.
Reduce the mixer speed and incorporate the powdered sugar. Mix well until the texture is homogeneous.

Decoration:
Use a fluted tip and cover almost the entire cake with frosting, then add some grated carrots on top.