Add quinoa and water to a medium pot, cover, bring to a boil, reduce heat to a low-boil and cook until quinoa has absorbed most of the water, approximately 12-15 minutes. Turn off heat and leave quinoa on the burner for 5 minutes.
While quinoa is cooking, place mushrooms gill (open side) up on a cookie sheet. Brush mushrooms with olive oil and evenly drizzle with balsamic vinegar. Season with salt to taste. Cook mushrooms 10 minutes. Drain excess liquid from mushrooms.
In the meantime, in a medium mixing bowl, combine cooked quinoa, black pepper, red pepper flakes, salt to taste, tomatoes, bread crumbs, basil and feta cheese.
Remove mushrooms from oven and evenly divide quinoa mixture, approximately 1/2 cup, into each mushroom. Bake 12 minutes or until mushrooms are tender and cheese is melted. Eat immediately or allow to cool slightly.