Dumbbell hammer curls are a great exercise you can do at home to finish your biceps training with, providing the added benefit of getting in some forearm training as well.
The Dumbbell Hammer Curl
I like to do dumbbell hammer curls as a finisher to my biceps training, because due to the exercises I did before, my biceps at that point of time usually are pretty exhausted.
Dumbbell hammer curls shine here because they still involve the biceps, but a large portion of the work is taken over by the forearms:
If you do the exercise with both arms at the same time or one after the other is entirely up to you. Personally I prefer to do one arm then the other, as I feel it helps me concentrating better on each movement.