Bring a large saucepan of generously salted water to a boil. Add quinoa and boil, stirring occasionally, until tender, 10 to 15 minutes.
Meanwhile, whisk the shallot, vinegar, mustard, oil and a generous pinch of salt and pepper in a very large bowl. When quinoa is done, drain very well, then add to the dressing, along with the chicken, cranberries and parsley. Fold until evenly mixed and cooled, then season to taste with salt and pepper.
Divide the salad among dishes and top with the chopped almonds and avocado.
It’s fastest and easiest to rinse grains in a sieve. Simply run cold water over them while gently shaking the sieve, then gently shake dry. It’s important to rinse grains to clean them and in the case of quinoa, to remove saponins, which can leave a bitter or soapy aftertaste. As it’s also tough to get flavors into grains once they’re cooked, it's a good idea to season them with salt at this point.