Preheat oven to 375 degrees F.
In a medium pot combine 1/3 cup quinoa (dry, pre-rinsed) and 2/3 cup water. Cover, bring to a boil, then reduce heat to low and simmer until the quinoa has absorbed most of the water, about 12–15 minutes. Turn off the heat, leave the pot covered for 5 minutes, then uncover and fluff the quinoa with a fork.
While the quinoa cooks, place the 4 portobello mushrooms gill (open side) up on a cookie sheet. Brush the mushrooms with 1 tablespoon olive oil, drizzle evenly with 2 tablespoons balsamic vinegar, and season with kosher or sea salt to taste.
Bake the mushrooms in the preheated oven for 10 minutes. Remove from the oven and drain any excess liquid from the mushroom caps and the cookie sheet.
In a medium mixing bowl combine the cooked quinoa, 1/2 teaspoon black pepper, 1/4 teaspoon crushed red pepper flakes, kosher or sea salt to taste, 1 cup diced vine-ripe tomatoes, 1/2 cup whole-grain bread crumbs, 1/4 cup freshly chopped basil, and 1/2 cup fat-free feta cheese. Stir until evenly mixed.
Evenly divide the quinoa mixture among the 4 mushrooms (about 1/2 cup mixture per mushroom), mounding it in the caps.
Return the filled mushrooms to the oven and bake 12 minutes, or until the mushrooms are tender and the cheese is melted.
Remove from the oven and serve immediately, or allow to cool slightly before serving.