Heat olive oil in a large saucepan over medium-high heat. Add carrots, red bell peppers, green bell peppers, onion, and shallot. Cook and stir until softened, about 5 minutes. Add garlic; cook and stir until fragrant, about 3 minutes.
Pour vegetable broth and quinoa into the saucepan. Cover and simmer until quinoa is soft, about 20 minutes. Sprinkle dried basil on top.