Coat the bottom and side of the top pan of a double boiler with 2 tablespoons of the soft butter. Heat water in the bottom pan to simmering. Beat the eggs just until well mixed and add the seasonings and the remaining soft butter. Fit the top pan into the bottom and stir the eggs with a wooden spoon for about 8 minutes, making sure to scrape all the surfaces of the pan, especially the corners. Never stop stirring or let the eggs stick to the pan. If the eggs start to thicken too quickly, remove the top pan from the water for a minute or so. When they are nearly done, stir in the cream and cook 30 seconds more. Turn off the heat and stir in the chilled butter; this will stop the cooking as well as enrich the texture and taste of the eggs.
Spoon the eggs onto 4 hot plates and serve immediately with non-sour country bread or grilled brioche.