Place the fiddleheads into a saucepan and cover with water. Bring to a boil over high heat, then reduce heat to medium-low, cover, and simmer until tender, about 15 minutes. The water will turn brown. Drain, and set aside.
While the fiddleheads are boiling, fill a large pot with lightly salted water and bring to a rolling boil over high heat. Once the water is boiling, stir in the spaghetti, and return to a boil. Cook the pasta uncovered, stirring occasionally, until the pasta has cooked through, but is still firm to the bite, about 12 minutes. Drain well in a colander set in the sink.
Heat the olive oil in a large skillet over medium heat. Cook and stir the garlic until fragrant, then stir in the smoked clams. Stir in the drained fiddleheads, white wine, and salt. Cook until heated through, about 5 minutes. Toss with spaghetti, and serve with Parmesan cheese.
