Cover brisket with water in a large pot or casserole. Add spices. Bring water to a boil and remove from heat. Wipe the inside of pot or casserole with a paper towel, being careful not to burn your fingers. Return pot to heat and simmer for 45 minutes per pound. Before the last 45 minutes of cooking time, adjust soup for saltiness by removing liquid and adding water if necessary. Add potatoes for the last 45 minutes of cooking time and the cabbage and asparagus for the last 15 minutes of cooking time.
Serve with rice.