Boil or steam fiddleheads for 15 minutes, immerse in ice water bath, drain and set aside.
Cook fettuccini according to package directions. Reserve 1/2 cup of the pasta water
Heat a medium skillet and add olive oil and butter. Add leeks and shallot, saute´ until softened but not brown. Add red pepper flakes and garlic and saute´until fragrant, about 1 minute. Add mushrooms and cook until golden brown in colour, about 4 minutes.
Add flour and cook, stirring for 1 minute. Slowly add the wine and cook until reduced, about 3 minutes. Add chicken stock and cook until thickened, about 5 minutes.
Add the fiddleheads and goat cheese and stir to combine and melt the cheese to make a creamy sauce.
Add the cooked pasta to the skillet and toss to combine. Add enough pasta water to reach desired consistency.