Preheat oven to 350 F.
Use a large saucepan to melt the butter over medium low heat. Stir in the flour to make a roux. Continue stirring for about three minutes.
Remove from the heat and add the milk in a slow, steady stream, whisking constantly.
Add the salt, pepper and cayenne. Simmer the sauce, stirring now and then, for about 8 minutes, or until it begins to thicken. Remove from heat and permit it to cool.
Beat the egg yolks in a medium bowl and add 1/2 of a cup of the sauce in a gradual stream, whisking constantly.
Stir in the minced fiddleheads and the cheese.
Using a large bowl, beat the egg whites with the cream of tartar until they become stiff, but not dry.
Stir about a fourth of the whites into the fiddlehead mixture. Then fold in the rest of the egg whites very gently and softly, to retain as much air in the whites as possible.
Heat a buttered 2 quart soufflé dish in oven until it is hot. Remove the dish before the butter browns.
Spoon the fiddlehead mixture into the bowl, smoothing the top.
Bake the soufflé in the lower part of the oven for about 45 minutes.
A cake tester inserted in the middle of the soufflé should come out clean.