Melt the coconut oil in a large saucepan with a tight-fitting lid over medium heat. Add thyme, leeks and garlic; cook for 5 minutes. Add ground beef; cook for 10 minutes, chopping it up into small pieces with a spoon.
Add remaining ingredients (mushrooms through cumin). Reduce heat, cover and simmer soup for 20 minutes or until beef is cooked through and vegetables are tender.