Heat the olive oil in a large pot over medium heat. Add the garlic, ginger, and scallions. Sauté for about 3 minutes, until very fragrant but not browned.
Add the oregano, parsley, cayenne, turmeric, black pepper, and soy sauce. Cook for 2 minutes, until the herbs begin to wilt.
Add the broccoli and cook until bright green and beginning to release some moisture, about 5 minutes.
Add the chicken stock. Cover, reduce the heat to low, and simmer for about 10 minutes, until the broccoli starts to soften.
Add the Swiss chard and stir until wilted, about 30 seconds. Add the baby spinach, a few handfuls at a time. Cook until just wilted and stir to incorporate into the soup before adding more. Once the spinach is wilted and the broccoli stems can be easily pierced with a fork, remove the soup from the heat. It is important not to overcook the greens, as they will begin to lose their vibrant color and nutrients.
Cool the soup for 15 minutes, until it can be safely transferred to a high-speed blender, if using. With a standing blender or immersion blender, puree the soup briefly to combine, then add the avocado, lemon juice, and salt and blend until creamy, with no lumps remaining.
Enjoy the soup hot or cold, garnished with toasted pumpkin seeds and parsley, if desired.