Slice your leftover corned beef and cut into cubes.
Shred your cheese if you didn't buy it pre-shredded.
Wash and trim brussels sprouts, then slice or shred them. A mandolin set about 1/8” works best, but you can use a food processor with the slicing blade or cut them with a knife one a time. Think of how you cut cabbage for slaw, you can also buy it pre-shredded.
Heat a skillet on medium high and add a tablespoon of butter or oil of choice. Sauté the brussels sprouts until they start to turn brown, then add the minced shallots and continue to toss and cook until shallots are just starting to turn translucent (about 1-2 minutes). Remove from heat and set aside.
Meanwhile, Start water boiling in a large sauce pan and cook the pasta about 1-2 minutes less than package directions. You want the pasta to be al dente. Gluten free pasta can turn to mush very quickly. If using regular pasta, I still suggest at least one minute less than package directions.
In another smaller sauce pan, add milk, cream, butter, dry mustard, cayenne pepper and white pepper. Heat (not boil) until butter is melted and seasonings are incorporated. Add the cheese and stir until it’s all smooth and creamy.
Drain pasta, place back into large sauce pan, pour cheese mixture on top and stir until completely combined and smooth. Add cubed corned beef, brussels sprouts and shallots. Stir until combined and serve. See notes below.