In a medium saucepan, combine the potatoes, 1/2 teaspoon of salt, and enough water to cover by 1 inch. Bring to a boil and cook until just fork tender, about 12 minutes. Remove from the heat and drain. Return to the pan and cook for 1 minute, mashing with a potato masher or heavy whisk over medium heat. Add the cream, butter, remaining 1/4 teaspoon salt, and pepper and mash until smooth. Mix in the parsley.
Remove from the heat and spread on a plate to cool for the Wellingtons. (Note: the potatoes can be made in advance and refrigerated until ready to use in the other recipe.)