Rhubarb-Birch Syrup: Heat a medium skillet over high heat. Add the butter, swirl to coat the bottom of the pan. Add the onion and rhubarb and saute until soft, 4 to 6 minutes. Add the birch syrup, wine, and lemon juice. Stir, season with salt and pepper and cook until the liquid is reduced by 1/2, about 8 to 10 minutes (should have a syrupy consistency). Adjust seasoning.
Mussels: Heat a wok over high heat. Add the oil and swirl to coat the pan. When the oil shimmers, add the garlic and ginger and stir-fry until fragrant. Add the mussels, Thai birds, Korean chile flakes, and cook, covered, until mussels open. Make a bed of the grilled potatoes on a large platter. Place the mussels on top of the potatoes and drizzle the birch/rhubarb syrup on and around the mussels. Toss the fiddleheads in the remaining mussel cooking liquid for a few seconds to warm them through. Top the mussels with the fiddlehead salad and sprinkle with more Korean chile flakes and the chives. Serve.
Potatoes: In a large bowl, combine the potatoes, garlic, and oil, toss to coat. Prepare a grill and cook the potatoes until crispy, about 10 to 15 minutes, turning half way through.