In a wide skillet over medium-high heat, warm the Granulated Sugar (1 teaspoon). Add in Olive Oil (1 tablespoon) and Yellow Onion (1/2 cup) and cook until they begin to brown, 10-15 minutes.
Add in Caraway Seeds (1/8 teaspoon), Green Cabbage (3 cup), Garlic (2 clove), Salt (to taste). and Ground Black Pepper (to taste). Cook for another 5 minutes.
Add Water (1/2 cup) and Worcestershire Sauce (2 teaspoon) to deglaze the pan. Cover and let the cabbage cook for another 15 minutes.
Prepare the sandwiches. Spread Mayonnaise (2 tablespoon) on one side of each slice of Dark Rye Bread (4 slice). This will be the side that lays on the pan.
On the other side of the bread, spread Whole Grain Mustard (1 tablespoon). Layer the sandwiches with Corned Beef Brisket (4 ounce), cabbage mixture, and Irish Cheddar Cheese (1 cup). Stack the other slice of bread on top mayonnaise side out.
Cook the sandwiches in a wide skillet over medium heat. Cook for 3-5 minutes on each side.
Serve warm with pickles and chips.