Add mushrooms, tarragon and parsley, saut until tender. Remove from heat, cool slightly. While still warm, transfer saut ed mushrooms to a mixing bowl. Add Boursin cheese and toasted pinenuts. Combine eggs and milk, mix until smooth.
Portion eggs into lightly oiled omelette pans and cook until set.
Spoon the mushroom mixture into the center of each omelette. Add a small amount of the shredded jack cheese. Fold the omelettes out onto warm serving plates. Top each with additional shredded jack cheeses and minced chives. Chef Larry's Notes Boursin is a garlic herb cheese, available in most markets.