The quinoa adds protein as well as a chewy texture to this meatless main dish. The heat of the cooked quinoa and mushrooms helps wilt the spinach; the dressing and feta pull this warm salad together.
Heat broiler; set rack 4 inches from heat. In a small bowl, whisk together vinegar, oil, 1 teaspoon salt, and 1/4 teaspoon pepper.
On a large rimmed broiler-proof baking sheet, toss mushrooms with half the dressing (reserve the rest); broil, tossing occasionally, until most of the liquid has evaporated and mushrooms are tender, 20 to 25 minutes.
Meanwhile, in a small saucepan, combine quinoa, 3 cups water, and 1 1/2 teaspoons salt. Bring to a boil; reduce heat to medium. Cover, and simmer until liquid has been absorbed, 15 to 20 minutes.
Place spinach in a large bowl; add hot mushrooms, quinoa, and reserved dressing. Toss to combine (spinach will wilt slightly). Top with crumbled feta, and serve immediately.
Do not soak shiitakes in water because they will become spongy. Instead, wipe the caps clean with a damp paper towel after trimming away the stems.