Preheat oven to 375°F.
Wash the quinoa in a fine mesh strainer under running water and then shake off the excess. Bring water to a boil in a small saucepan and whisk in quinoa. Simmer, covered, until water is absorbed and quinoa is tender, 10 to 15 minutes. Drain any excess water from pan and let cool. Meanwhile, heat oil in a large nonstick skillet and cook onion, celery and carrot over moderate heat, until softened, about 4 minutes. Add mushroom and garlic and cook, stirring occasionally, until liquid mushrooms give off are evaporated and vegetables are tender, about 10 minutes. Let mixture cool. Place beef in a large bowl and mix with cooled vegetables, quinoa, parsley, eggs, and Worcestershire sauce with salt and pepper until just combined (do not over mix). Form mixture into loaf (9- by S-inches) onto a lightly greased sheet pan and roast in middle of
oven for 30 minutes. Remove from oven and spread ketchup on top and sides of meat and continue to roast for another 30 to 45 minutes until meat registers 155°F on an instant-read thermometer. Let meat stand for 10 minutes before slicing.