In a medium pot with steamer tray, steam broccoli just until tender and set aside.
To make brown rice: In a saucepan over medium-high heat, combine the brown rice, water and salt and bring to a boil. Reduce the heat to low, cover, and cook for 45 minutes, or until the water is absorbed. Set aside, covered, to steam for 5 minutes. Fluff with a fork. Set aside.
To make the stir-fry: In a large skillet over medium-high heat, heat the oil and swirl the pan to coat. Add onions and garlic and sauté for 1 to 2 minutes or until onions start to become translucent. Add chicken and tamari and cook for 4 to 6 minutes. Add carrots, peppers, snow peas and chicken broth. Cook for an additional 3 to 4 minutes. Add broccoli, spinach and ginger and cook until spinach is wilted approximately 2 to 3 minutes or until chicken is done.
Fluff the reserved rice with a fork and divide among 4 bowls. Spoon the stir-fry mixture over the rice and serve.