Combine the quinoa with the broth in a large saucepan. Bring to a rapid simmer, then lower the heat, cover, and simmer gently until the water is absorbed, about 15 minutes. Test to see if the quinoa is done to your liking; if needed, add another ½ cup water and simmer until absorbed.
Meanwhile, heat the oil in a large skillet or stir-fry pan. Add the onions and sauté over medium-low heat until translucent. Add the garlic and continue to sauté until the onion is golden.
Add the cabbage, carrots, broccoli, mushrooms, ginger, basil, thyme, and lemon juice. Turn the heat up to medium-high and stir-fry until the cabbage is tender-crisp, about 5 minutes.
Stir in the cooked quinoa, then season to taste with salt and pepper. Stir in the parsley and dill, remove from the heat, and serve.