Add potatoes to a large saucepan and cover with 1-inch water. Bring to boil over high heat. Reduce heat to medium and simmer until potatoes are almost tender, 8-10 minutes. Drain potatoes and set aside until cool enough to handle. Cut potatoes in half lengthwise.
In a large frying pan, heat oil over medium-high heat. Add potatoes and cook, tossing occasionally until well-browned, 8-10 minutes.
Meanwhile, mix together cream cheese and chives until combined. Season with salt and pepper, to taste.
Top each potato half with a dollop of cream cheese, a piece of salmon and sprig of dill.