In a small saucepan melt the butter over medium-high heat.
Add the flour and cook for about 1 minute.
Whisk in the milk and continue to whisk until the sauce thickens and comes to a boil, about 2 to 3 minutes.
Reduce to a simmer and season with the salt, pepper and nutmeg. Simmer for 2 to 3 more minutes.
Stir in the Gruyere until melted. Keep warm.
While Mornay is simmering, add 1 T. butter to small nonstick saute pan over medium-high heat.
Saute shallots and bell pepper for a couple minutes. Add lobster meat and continue to saute for a few minutes or until lobster meat is opague in color. Remove from pan. Keep warm.
Crack the warm eggs into a bowl, add salt and blend with a fork.
Heat the same pan over medium-high heat.
Add 1 tsp. butter and cover pan.
Pour the eggs into the pan and stir with a rubber spatula for 5 seconds.
Lift the pan and move it around until the excess liquid pours off into the pan under the cooked egg.
Loosen the egg from the pan with the spatula.
Add lobster mixture to one side of the omelette and flip the other side over to cover.
Slide onto a plate and cover with the Mornay sauce.
Garnish with chives. Say Grace and serve immediately!