Start by rinsing the quinoa under cold water. In a large pot, combine quinoa and water, bring to a boil, reduce heat, cover, and simmer for about 15 minutes.
Preheat your oven to 375°F (190°C). Prepare portobello mushrooms by removing stems and scraping out gills. Place caps on a baking sheet.
In a mixing bowl, combine cooked quinoa, diced tomatoes, bread crumbs, chopped basil, and half of the feta cheese. Add olive oil and balsamic vinegar, season with black pepper, red pepper flakes, and salt. Mix thoroughly.
Spoon the quinoa mixture into each portobello cap, pressing down slightly. Top with remaining feta cheese.
Bake the stuffed mushrooms for 20-25 minutes, or until tender and tops are golden.
Let cool for a few minutes before serving. Enjoy warm or at room temperature.