Preheat oven to 425°F. Heat 1 tablespoon oil in a medium saucepan over medium-high. Smash 1 of the garlic cloves. Add couscous and smashed garlic to saucepan; cook, stirring often, until golden brown, 2 to 3 minutes. Add 1 ½ cups water and 1 teaspoon salt. Bring to a boil over medium-high. Cover and reduce heat to medium-low; cook, undisturbed, until tender, about 14 minutes. Remove from heat, and fluff using a fork.

Meanwhile, toss together broccoli florets, 2 tablespoons oil, 1 teaspoon salt, and crushed red pepper on a large rimmed baking sheet; spread in a single layer. Roast the broccoli in the oven until tender but not browned, 12 to 15 minutes.

Sprinkle chicken evenly with pepper and 1 teaspoon salt. Place za’atar seasoning in a wide, shallow bowl. Dip chicken in za’atar until evenly coated.

Heat 2 tablespoons oil in a large nonstick skillet over medium-high. Working in 2 batches, cook chicken until light golden brown, about 2 minutes per side. Transfer to the baking sheet with the broccoli. Wipe skillet clean between batches; repeat process with remaining 2 tablespoons oil and chicken. Transfer baking sheet to the oven and cook until the broccoli is lightly charred and the chicken registers 165°F with an instant-read thermometer inserted into thickest portion of, 5 to 7 minutes.

Grate remaining garlic clove. Whisk together tahini, 2 tablespoons of the lemon juice, and remaining 3 tablespoons water, ½ teaspoon salt, and grated garlic in a small bowl.

Toss together parsley, mint, and remaining 1 teaspoon oil and 1 teaspoon lemon juice in a medium bowl. Season to taste with additional salt and pepper. Serve parsley salad with chicken, broccoli, couscous, tahini sauce, and lemon wedges.