Bring water and quinoa to the boil in a saucepan. Reduce heat to medium-low; cover and simmer until quinoa is tender, 15 to 20 minutes.
Heat 1 teaspoon olive oil in a casserole pot over medium-high heat. Add chicken; season with salt and pepper. Cook and stir until chicken is no longer pink in centre, about 5 minutes. Transfer chicken to a plate.
Heat remaining 1 teaspoon olive oil in the casserole pot over medium heat. Add onion, carrots, celery, red pepper, yellow pepper and garlic; cook and stir until soft, about 10 minutes.
Pour chicken stock into the casserole pot. Add spinach leaves, marjoram, oregano, basil and bay leaf. Bring to the boil; reduce heat and simmer until flavours combine, about 10 minutes. Stir in cooked quinoa. Return chicken to the casserole pot; cook until heated through, about 2 minutes.
Dissolve cornflour in cold water in a small bowl. Pour slowly into the casserole pot; cook, stirring occasionally, until soup thickens, about 1 minute.