Using a food processor, pulse the cauliflower until it is in rice-sized pieces. You may want to do this in batches for consistent results. Pour into a bowl and set aside.
In a large sauté pan, heat the coconut oil over medium-high heat. Add the cubed tofu, cover and cook, stirring occasionally, until browned. Transfer tofu to a small bowl and set aside.
Add the green onions and garlic to the sauté pan. Reduce heat to medium and cook until aromatic, about 2 minutes. Add the mushrooms, ginger and a splash of vegetable broth. Cook, stirring occasionally, until soft and browned, about 5 minutes.
Add the remaining ingredients, including the cauliflower rice, tofu and remaining vegetable broth, and cook until kale is wilted and everything is heated through, about 5 minutes. Serve immediately.