Whisk eggs and heavy cream together in a large bowl.
Heat a large nonstick skillet over medium heat. Spread butter evenly over the surface of the pan; cook until foamy, 30 seconds to 1 minute. Add eggs; cook until beginning to set, about 4 minutes. Drop cream cheese pieces, salmon pieces, and scallions over the eggs. Continue cooking until eggs are set, about 2 minutes more. season with salt and pepper.
Roll the omelet over onto itself; slide onto a plate. Top with dill, sour cream, and chives.