Heat the oil in a large soup pot over medium-high heat. Add the mushrooms and a pinch of salt, toss to coat, and arrange in a single layer. Cook until golden where the mushrooms meet the pan. Toss, and cook a couple more times, or until the mushrooms are deeply browned, five minutes or so. Remove from the pan and set aside.
Using the same pan, stir in the onion, adding a bit more oil if needed. Sauté the onions, and after a few minutes, stir in the ginger, and chile flakes. After another minute or so, add the garlic, and the kimchi. Sauté until the garlic is deeply aromatic. Add the water, and the honey or sugar.
At this point, stir in the broccoli, and simmer for a minute, or just until the broccoli becomes bright green. Remove the soup from heat. Place the miso in a small bowl and whisk a splash of broth into it, to thin it out. Stir the thinned miso, and the reserved kimchi juice into the soup. Taste. If the broth tastes a bit flat, add more salt, or miso, or a splash of shoyu/soy sauce.
Just before serving, drizzle the tofu with a bit of shoyu/soy sauce. Serve the soup ladled into bowls, topped with the tofu, mushrooms, and as many of the suggested toppings as you can pull together - green onions, sesame seeds and a squeeze of lemon or lime juice.