Separate cabbage leaves and stems. Cut leaves into 3cm pieces and stems into 4cm sticks. Slice onion into 1cm thick pieces.
In a pot, combine all A ingredients. Add the vegetables and beef. Bring to a boil over high heat, skim off any scum, then reduce to medium heat and add the udon. Simmer until cooked through.
Transfer to serving bowls. Top with green onions and drizzle with sesame dressing.
Tips
Top with a soft-boiled egg, shichimi togarashi, or grated ginger for added flavor.