In a medium saucepan, combine the rinsed quinoa and water. Bring it to a boil over medium-high heat. Once boiling, reduce the heat to low, cover, and let it simmer for about 15 minutes or until the quinoa is fluffy and the water is absorbed. Remove from heat and let it sit covered for 5 minutes.
While the quinoa is cooking, preheat your oven to 375°F (190°C).
Gently clean the portobello mushroom caps with a damp cloth. Remove the stems and any visible gills using a spoon or knife.
In a mixing bowl, combine the cooked quinoa, diced tomatoes, whole-grain bread crumbs, chopped basil, feta cheese, olive oil, balsamic vinegar, black pepper, crushed red pepper flakes, and salt. Mix everything until well combined.
Spoon the quinoa mixture generously into each portobello cap, pressing down gently to pack the filling. Place the stuffed mushrooms on a baking sheet lined with parchment paper.
Bake the stuffed mushrooms in the preheated oven for about 25-30 minutes or until the mushrooms are tender and the tops are slightly golden.
Once baked, remove the mushrooms from the oven. Allow them to cool for a few minutes before serving.