Preheat the oven to 425°F (220°C). Line two rimmed baking sheets with parchment or lightly oil them so the vegetables and chickpeas roast, not steam.
Toss the drained chickpeas with 1/2 tablespoon olive oil, smoked paprika, and a pinch of salt. Spread them in a single layer on one prepared sheet so they crisp up while roasting.
On the second sheet, combine the bell pepper, zucchini, red onion, and cherry tomatoes. Drizzle with 1 tablespoon olive oil, sprinkle 1/2 teaspoon kosher salt and a few grinds of black pepper, then toss to coat evenly. Arrange vegetables cut-side down where appropriate for good caramelization.
Roast both sheets on the middle rack for 20 to 25 minutes, switching the pans between racks halfway through and stirring the chickpeas once. Vegetables should be browned at the edges and tender; chickpeas should be slightly crispy.
While the vegetables roast, rinse the quinoa under cold water. Combine rinsed quinoa and 2 cups water (or broth) in a medium saucepan with 1/4 teaspoon salt. Bring to a boil, reduce heat to low, cover, and simmer gently for 12–15 minutes until water is absorbed.
Remove the pot from heat and leave covered for 10 minutes to steam. Fluff the quinoa with a fork to separate the grains.
Make the dressing by whisking together 3 tablespoons olive oil, lemon juice, minced garlic, za'atar, remaining 1/2 teaspoon salt, and black pepper. Taste and adjust acidity or salt as desired.
Place the warm quinoa in a large bowl, pour half the dressing over it and toss to coat. Add the roasted vegetables and chickpeas while still warm so they absorb flavor; drizzle remaining dressing and stir gently until everything is evenly mixed.
Divide the quinoa and roasted veg among bowls. Top with crumbled feta and chopped parsley. Serve immediately with lemon wedges for extra brightness.