In a medium pot of salted water, bring potatoes to a boil and cook until knife-tender, about 8 minutes. Add fiddleheads and cook until bright green, about 1 minute. Drain and set aside.
Heat oil in a medium skillet over medium-high heat and cook shallot until golden, about 2 minutes. Add potatoes and fiddleheads and cook, stirring, until golden brown, about 4 minutes. Season with salt and pepper.