If making this for a celebration for St. Paddy's day, go ahead and cut out your Shamrock bread to make toast.
Beat your eggs and milk in a bowl with a little salt & pepper. Add to a heated pan w/hot oil and pour in. Now, swirl around a litte so that your omelet cooks evenly. Lift up the edges of egg mixture with spatula to allow uncooked egg to run under. Once it is almost cooked through add your hot corned beef, kraut on top and then squirt on your Thousand Island dressing.
Fold over omelet in pan....this is a heavy omelet so use 2 spatulas so that it doesn't tear like mine did. No worries though if it does as you are going to add a swiss cheese sauce on top. Yumm
Meanwhile, heat your butter on medium/low heat in a small pan and then add your flour; stir till combined. Then add your 1/4 cup of half and half and continue to stir. Add, your seasonings and shredded Swiss cheese. Whisk till completely melted and is a nice "pour" consistency. If it is too thick add more half & half.
Since I live in a town with a few "Irish" folks, I was unable to find any Thousand Island dressing and found an amazing product called "Secret Burger Sauce". On the back of the bottle it reads: "Why go out to a burger joint when you enjoy this bold twist on thousand island flavor at home?." ---This worked perfectly!