Slice the Corned Beef Brisket (6 ounce) and Swiss Cheese (4 slice) if not pre-sliced.
Juice the Lemon (1/2). You will need 1 teaspoon of juice.
To make the aioli, mix Mayonnaise (1/4 cup), 1 teaspoon lemon juice, Cocktail Sauce (2 teaspoon), Ground Black Pepper (1 dash), Ground Coriander (1/4 teaspoon), and Dried Dill Weed (1/4 teaspoon) in a small bowl. This makes enough to spread onto both sandwiches' slices of bread. If you prefer to have more for dipping, double the recipe and serve remaining aioli in small dish.
Spread Butter (3 tablespoon) one side of each slice of Rye Bread (4 slice). Turn butter side down onto your work surface.
Spread aioli on the other sides of each slice of bread. Divide between the two sandwiches and top each with the Sauerkraut (1/2 cup), corn beef brisket, and swiss cheese. Put the halves together.
Heat a medium-sized skillet to medium heat. Lay sandwiches into pan and fry on each side until golden brown, around 5-10 minutes. Serve immediately.