Melt the butter in a large skillet over medium heat.
Add the diced onion, rinsed quinoa, and minced garlic to the skillet and cook, stirring occasionally, until the onion is soft and translucent, about 3–5 minutes.
Pour in the chicken broth and half and half, then add the drained diced tomatoes and salt. Stir to combine.
Bring the mixture to a boil, then reduce heat to low, cover, and simmer for 15–20 minutes, or until most of the liquid is absorbed and quinoa is tender.
Stir in the chopped basil and Parmesan cheese until melted and evenly distributed.
If the cooked chicken is cold, add the sliced chicken on top of the quinoa, cover, and warm for a few minutes; otherwise, stir the chicken into the quinoa to combine and heat through.
Serve topped with additional Parmesan and basil if desired.