In a saucepan of boiling salted water, blanch the fiddleheads for 2 minutes. Drain and rinse in cold water. Set aside.
In a skillet, cook the bacon until golden. Remove the fat. Add the onion and cook until tender. Add the fiddleheads and chives. Continue cooking for 1 to 2 minutes. Set aside.
In a bowl, mix the eggs, cream and parsley. Salt and pepper.
In a hot, 8 inch (20 cm), non-stick skillet, melt 1 1/2 tsp (7.5 ml) of butter.
Pour 1/4 of the eggs into the skillet. Cook over medium heat and puncture the bottom of the omelette with a spatula to facilitate cooking. Salt and pepper.
When the edge of the omelette is almost cooked, but not the center, put ¼ of the filling and part of the crumbled cheese on one half of the omelette.
Using a spatula, fold the omelette toward the filling and slide onto a plate. Keep warm.
Repeat the same operation for the other three omelettes.