In a non-stick 10-inch saute pan over medium-high heat, heat the butter. Add the mushrooms and saute for 5 minutes. Meanwhile, beat together the eggs, heavy cream, salt, and pepper. Lower the heat to low.
Add the egg mixture to the pan. Cook the eggs for 5 minutes, or until they start to set up. Remove the pan from the heat. Sprinkle the cheese over the top of the eggs and place the pan under the broiler. Broil for 5 minutes until the eggs have cooked and the cheese is melted. Remove the frittata from the pan onto a cutting board. Sprinkle the frittata with chives. Cut the frittata into 1 1/2-inch pieces. Top each piece with a dollop of creme fraiche and caviar.