Preheat oven to 400 degrees. Butter one side of a 12-inch square of parchment paper; set aside.
Heat oil and butter in a medium ovenproof skillet over medium heat. Add shallots and saffron and cook until shallots are translucent. Add potatoes and cover with fish stock; raise heat to medium-high. Place parchment paper over potatoes, butter side down and bring to a boil.
Immediately transfer skillet to oven and cook until potatoes are tender, about 10 minutes.