How to Make It
In a medium bowl, mix together the yogurt, garlic, lemon juice, ¼ teaspoon salt, and ⅛ teaspoon pepper. Add the chicken and turn to coat. Refrigerate for at least 30 minutes and up to 2 hours.
Heat oven to 450° F. Spread the walnuts on a rimmed baking sheet and toast, tossing occasionally, until fragrant, 4 to 5 minutes. Let cool and coarsely chop.
Meanwhile, cook the quinoa according to the package directions. Fold in the walnuts, parsley, 2 teaspoons of the oil, ½ teaspoon salt, and ⅛ teaspoon pepper.
Divide the potato, mushrooms, and thyme between 2 rimmed baking sheets; toss with 1 tablespoon of the remaining oil, ½ teaspoon salt, and ⅛ teaspoon pepper. Roast, rotating the sheets once, until tender, 13 to 15 minutes. Drizzle with the vinegar and toss gently.
Heat the remaining 1 teaspoon of oil in a large cast-iron or other nonstick skillet over medium heat. Wipe the excess marinade off the chicken and cook until golden brown and cooked through, 3 to 4 minutes per side. Serve with the quinoa and vegetables.