Cook 1 cup quinoa and 1/2 cup millet in boiling salted water until tender, about 12 minutes. Drain and spread on a paper towel?lined baking sheet to cool. Cook 8 ounces sliced shiitake mushrooms in olive oil in a large skillet over medium-high heat until browned, 5 minutes. Add 1 cup corn, 1 teaspoon fresh thyme and salt and pepper to taste; cook, stirring, until the corn is tender, 30 seconds. Let cool, then toss with the grains, 1 cup fresh parsley, the juice of 1/2 lemon and 3 to 4 tablespoons olive oil. Stir in 1/2 cup shredded parmesan.