For the brisket: Set oven to broil. Dredge the brisket in flour and season with salt and pepper. Sear the brisket for 5 minutes on each side, until brown.
Set the oven to 325 degrees F. Coat the roasting pan with cooking spray, place seared brisket in pan. Place the carrots, onions, and garlic around the brisket in the pan.
Mix the ketchup, water, soy sauce, vinegar, and Worcestershire sauce and stir. Pour the mixture over the brisket and vegetables. Cover tight with heavy tin foil. Cook for 3 to 4 hours. After the brisket has been in the oven for 2 to 3 hours, take out and add crumbled the ginger snap cookies into the liquid that surrounds the brisket. Mix around so the sauce gets thicker. Put back in oven, uncovered, for the remaining 1 hour.
When the cooking is complete, take out of oven and let rest for 1 hour. Slice thin and put in the refrigerator overnight.
Reheat and serve the next day.
For the sandwich: Toast the light rye bread. Place the cheese on one slice of bread and melt in microwave. Spread the caramelized onions on top of the melted cheese. Put sliced brisket on top of the onions. Top with coleslaw, then with pickles and the other slice of bread.
Cook's Note: The combination of the hot and the cold, the sweet and the sour, the spicy and the savory, the beginning of a new year and the end of the past year.