Preheat oven to 40OF (205C). In a medium-size bowl, beat half and half and flour together until smooth. Add eggs one at a time, beating well after each addition. Season well with salt and pepper. Beat vigorously until creamy.
Melt butter in an 8-inch omelet pan over low heat. Pour in batter and cook 2 minutes. Transfer to oven and bake 8 minutes. Top with smoked salmon and serve immediately. Do not fold this omelet. If desired, garnish with a slice of lemon, a sprig of dill and a salmon cone filled with caviar.