Heat olive oil in a soup pot over medium heat. Add garlic; cook and stir 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. Add collard greens; cook and stir until wilted, about 5 minutes.

Add black-eyed peas and pour in vegetable broth; bring to a boil. Reduce the heat to low, cover, and simmer until vegetables are softened, 20 to 25 minutes.

Meanwhile, bring water and quinoa to a boil in a medium saucepan. Reduce the heat to low, cover, and simmer until all water has been absorbed, about 10 minutes.