Preheat the oven to 425 degrees F (220 degrees C). Line a baking sheet with aluminum foil.
Spread cherry tomatoes on the prepared baking sheet. Drizzle with 1 tablespoon olive oil. Sprinkle salt and pepper over tomatoes and toss to coat evenly.
Roast in the preheated oven until tomatoes blister and pop and skins start to char, 15 to 20 minutes.
Meanwhile, heat remaining olive oil in a large Dutch oven over medium-high heat. Add onion and cook until translucent, 4 to 5 minutes. Add garlic, paprika, cumin, coriander, cayenne pepper, salt, and pepper. Cook until fragrant, 30 to 60 seconds. Add tomatoes and green chiles; bring to a boil. Reduce stew to a simmer and add chickpeas. Add the cherry tomatoes and their juices. Cover and simmer for 30 minutes.
While stew simmers, bring 3 cups water and quinoa to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until quinoa is tender, 15 to 20 minutes.
Mix Greek yogurt, hummus, 1 tablespoon water, and vinegar together to make the sauce. Season with salt and pepper.
Serve the stew over quinoa. Top with the yogurt sauce, green onions, and cilantro.