Grating the carrots on the large holes of a grater is key. Otherwise, the shreds are too fine and become lost in the salad. Slideshow: More Quinoa Recipes
Bring water to boil in a large saucepan. Add 1 teaspoon salt and the quinoa. Cook until the quinoa is just tender, 15 to 20 minutes. Drain the quinoa.
Meanwhile, in a large bowl, add shallot, lemon juice, and 1/2 teaspoon salt. Let stand for 10 minutes.
To the large bowl, add the drained quinoa, carrots, olive oil and parsley. Stir. Season to taste with salt. Serve.
The salad can be prepared up to the parsley and refrigerated for two days. Add the parsley and more salt and lemon, if needed.