Rinse the quinoa in a fine sieve, then drain excess water. Place the drained quinoa in a frying pan over medium heat. It will take the water a few minute to evaporate, then as the quinoa dries, it will begin to toast. Stir periodically until the quinoa is evenly browned and gives off a lovely nutty aroma. Set aside 1/4 cup of the toasted quinoa.
Place the remaining 3/4 cup quinoa and 1 cup water in a saucepan and bring to a boil over medium heat. Lower the heat to a simmer, and cook for about 10 minutes. Cover and let the quinoa sit for 5 minutes more. The water should be fully absorbed. Drain any excess water if necessary.
While the quinoa cooks and cools, prepare the artichokes. Fill a large bowl with cool water, then squeeze the juice of two lemons into the water, and drop the lemons into water, as well. Remove the outer leaves of the artichoke by snapping them off, until you are left with the tender leaves within. Cut about 1 1/2 inches off the tops of the artichoke, then remove the purple choke inside by scooping it out with a spoon. Trim the stems of the artichoke, then peel the tough outer layer of the stem. Place the artichokes in the lemon water bath. Repeat with remaining artichokes.
In a medium bowl, combine the cooked quinoa, feta, parmesan, garlic, shallot, cilantro and parsley. Stir in the olive oil and toss to evenly coat the stuffing. Stuff the artichokes well with the stuffing, topping it with some of the reserved toasted quinoa, and place in a baking dish. Drizzle with a little olive oil and season with salt and pepper. Add a little water to the baking dish, cover with aluminum foil and bake the artichoke for about 45 minutes, or until a knife inserted into the artichoke heart shows that it is tender and fully cooked. Remove the foil and continue baking for 5 minutes more.