Grease the inside of 4 ramekins with butter, then place them inside a square baking dish.
Place smoked salmon in the bottom of each ramekin, then top with creme fraiche (or sour cream), and a scant 1 tsp fresh chopped dill. Place cracked egg into each ramekin, then drizzle a little heavy cream around each egg, about per portion. Season lightly with Kosher salt and freshly ground black pepper.
Pour boiling water into the baking dish surrounding the ramekins so that it comes up about ¾ way. Bake for 15-20 minutes, or until the eggs are cooked to your personal liking.
Carefully remove the baking dish, then use a thin spatula or tongs to remove each ramekin. Dry off the exterior of each ramekin as needed. Add more black pepper if you like.
Serve the oeufs en cocotte with toasted baguette or brioche sticks and chopped chives.