Put the whole smaller potatoes and halved larger potatoes in a pot, cover with water and bring to a boil over medium heat. Salt the water and cook until the potatoes are tender.
Drain the potatoes and return them to the hot pot on the stove. Add the butter; when it begins to melt, sprinkle in the paprika and the parsley. Toss to coat the potatoes with the butter mixture and transfer to a serving bowl.