Preheat the oven to 375°. Have a 9x13 baking pan or baking sheet ready. Wash and then break up the cauliflower into smallish pieces. Drizzle with 2 tablespoons olive oil and sprinkle with salt. Place in the oven and roast for about 45 minutes-1 hour.
Heat 1 tablespoon olive oil in a saucepan on medium-low and add the quinoa. Toast the quinoa until fragrant, stirring often, for a few minutes. Then add 2 cups water, 1 cup coconut milk, and ½ teaspoon salt to the quinoa. Bring it to a boil over high heat. Reduce heat to low, cover, and cook until quinoa has absorbed the liquid, about 15 to 20 minutes. Remove from heat.
While quinoa is cooking, heat 1 tablespoon olive oil in a large skillet over medium-high heat. When it shimmers, add the garlic, ginger and carrot and cook until starting to soften, about 5 minutes. Then add broccoli and cook, stirring frequently, about 2 minutes. When the cauliflower is done, add the cauliflower to the skillet and mix to incorporate.
Add the quinoa to the skillet and mix it in with the vegetables. Season with salt and pepper.