Prepare the filling by stirring Dijon mustard into chicken broth in a saucepan until dissolved. Bring to a simmer over medium-high heat, then add 1/4 cup cream and 2 tablespoons butter. Reduce heat to medium, and simmer until reduced by half, then stir in crab and shrimp; keep warm over low heat.
Prepare the sauce by warming 1/4 cup cream, and 1 teaspoon mustard over medium heat. Once hot, whisk in the shredded cheese, then season to taste with nutmeg, salt, and pepper. Keep warm over low heat.
Whisk eggs, 1/4 cup cream, salt, and pepper together until smooth. Heat an 8-inch non-stick skillet over medium heat, and lightly oil with cooking spray. Pour 1/4 cup of the egg mixture into hot pan, and swirl to make a thin, even layer of egg. Cook until firmed, then flip and cook for a few seconds more to firm the other side.
To prepare omelets, spoon some of the seafood filling into the lower half of each omelet. Roll up into a cylinder. Serve 2 per person bathed with Cheddar sauce.