Combine chicken stock and quinoa in a large pot over high heat; bring to a boil. Reduce heat to low and simmer, covered, until quinoa is tender, about 15 minutes. Remove from heat and let stand, covered, for 5 minutes.

Whisk lemon zest, lemon juice, olive oil, pepper, and salt in a small bowl to make lemon dressing.

Stir lemon dressing, chicken, water, diced tomatoes, feta cheese, half-and-half, carrots, pesto sauce, and oregano into the cooked quinoa. Cook over medium heat, stirring frequently, until thick and creamy, about 15 minutes. Spoon into individual bowls.