In a large skillet over medium-high heat, melt the butter. Season both sides of the chicken breasts with salt and pepper. Add to the skillet and cook for about 4 or 5 minutes on each side. Remove from skillet and set aside.
Lower the heat to medium. Add the onion and garlic to the same skillet and cook in the leftover juices until tender, about 3 minutes. Add the chopped tomatoes and continue cooking for about another 3 minutes.
Add the stock and heavy cream. Stir the mixture and raise the heat to high to bring it to a boil. Bring it back down to a simmer and stir in half of the freshly chopped basil leaves. Nestle the chicken breasts in the mixture. Cover and continue to simmer on low heat for about 15 minutes.
Serve your prepared quinoa on a serving plate, spread evenly. Once the chicken mixture is done, add the breasts individually, then spoon the remaining sauce over the top, making sure to include plenty of pieces of tomato. (You will likely have sauce leftover. Just reserve this for leftovers or as a supplemental side if anyone wants more.) Sprinkle with the remaining basil and the feta.