Begin by rinsing the quinoa under cold water to remove its natural coating. In a medium saucepan, combine the rinsed quinoa and water. Bring to a gentle boil, then reduce the heat to low and cover. Allow to simmer for about 15 minutes, or until all the water is absorbed. Fluff with a fork and set aside.
Preheat your oven to 375°F (190°C).
Carefully remove the stems from the portobello mushrooms and gently scrape out the gills. Brush each mushroom cap with olive oil on both sides and place them on a baking sheet, gill side up.
In a mixing bowl, combine the cooked quinoa, diced tomatoes, bread crumbs, chopped basil, feta cheese, balsamic vinegar, black pepper, crushed red pepper flakes, and salt. Mix until well incorporated.
Spoon the quinoa filling into each portobello mushroom cap, packing it lightly.
Place the stuffed mushrooms in the preheated oven and bake for 20-25 minutes, or until tender and golden brown on top.
Once baked, let them cool for a few minutes. Serve warm, garnished with extra fresh basil if desired.