Toss beef with 1 tsp. each soy sauce and sesame oil and cook, stirring, over medium heat in a small saucepan. Set aside.
Put stock, 1 tbsp. soy sauce, and 2 tsp. sesame oil in a large, heavy pot. Add fermented soybean paste (if using Japanese red miso instead, add just before serving) and stir to dissolve. Stir in garlic and chiles and bring to a boil, covered.
Add tofu, cabbage, zucchini, daikon, and two-thirds of the green onions; return to a boil, then lower heat and simmer, covered, until everything is tender, at least 5 minutes. Meanwhile, if using Japanese red miso, whisk with 1/2 cup hot broth. Stir miso broth, remaining green onions, and reserved beef into stew just before serving.
*Find at Korean markets. Japanese akamiso is available at gourmet grocery stores; you could also use white miso in a pinch.
Note: Nutritional analysis is per serving.