Heat olive oil in a soup pot over medium heat; cook and stir garlic until it begins to brown, about 3 minutes. Add onion and carrots. Cook and stir until carrots begin to brown and onion becomes translucent, 7 to 8 minutes. Cook and stir collard greens into onion mixture until wilted, about 5 minutes.

Pour vegetable broth and black-eyed peas into vegetables, bring to a boil, and reduce heat to low. Cover and simmer soup until vegetables are softened, 20 to 25 minutes.

While soup is simmering, mix quinoa and water in a saucepan, bring to a boil, and reduce heat to low. Cover and simmer until the water has absorbed into the quinoa, about 10 minutes. Stir cooked quinoa into soup and simmer until collard greens are tender, about 10 more minutes. Stir cider vinegar into soup to taste and season with salt and black pepper.