Cook the rice: In a small pot, bring the water to a boil. Add the brown rice, reduce the heat to simmer, and cover. Cook, covered, for 45 minutes while you follow the other steps.
Steam the broccoli: Steam the broccoli in a vegetable steamer until fork-tender (about 6 to 8 minutes for fresh broccoli; 10 to 12 minutes for frozen). Remove from heat, cover, and set aside.
Cook the aromatics: Add ¼ cup of the broth and the onion to a large pot or Dutch oven over medium heat. Cook the onion, stirring frequently, for approximately 6 to 8 minutes, or until softened. Add the garlic and chicken seasoning, and cook for 1 additional minute, stirring frequently. Add a splash of broth at any point if necessary to prevent sticking.
Cook the squash: Add 1 cup of broth to the pot, along with the butternut squash. Bring to a boil, then lower heat to a simmer. Cover and cook for approximately 8 to 10 minutes, or until the squash is soft.
Blend: Carefully add the contents of the pot to a blender, along with the rest of the broth, nutritional yeast, miso paste, mustard, lemon juice, and turmeric. Blend until smooth. Taste and add an additional 1 tablespoon of nutritional yeast, if desired (see Note).
Add the broccoli and rice: Pour the blended mixture back into the large pot (no need to rinse the pot first). Add the steamed broccoli and rice and stir. Taste and add an optional additional splash of lemon juice, a pinch of fine sea salt, and/or a few cracks of black pepper, if desired. Stir well and serve hot.