Place brisket in a large Dutch oven and cover with water. Add spice packet, bay leaves, and thyme and place on medium-high heat. Bring to a boil, then reduce to a simmer. Cook until tender, skimming occasionally and checking every 30 minutes and adding water if needed, until beef is tender, about 3 hours and 30 minutes.

Add potatoes and carrots and bring back up to a boil. Cook for 15 minutes, then add cabbage and boil 5 minutes more. 

Remove meat and drain vegetables. Let meat rest 10 minutes before slicing against the grain.