1. Cook the quinoa and millet in boiling salted water until tender, about 12 minutes. Drain and spread on a paper towel-lined baking sheet to cool (a big colander also works).
2. Cook the shiitake, onions and garlic in olive oil in a large skillet over medium-high heat until browned, about 5 minutes.
3. Add the corn, thyme and season with salt and pepper to taste. cook, stirring, until the corn is tender, 30 seconds. Toss in the grains, parsley and the lemon juice; drizzle with 3 to 4 tablespoons olive oil.