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, and 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.