In a stock pot or large skillet, sauté the tomatoes and onion in olive oil over high heat.
Add the cheeses, thyme, salt and pepper, and cook until the tomatoes break open and the juices meld with the feta and cheddar, about 5 minutes.
Working in several batches, add tomato juice and tomato-cheese mixture to the blender and puree until smooth. For a more rustic finish pulse the blender a few times instead to leave seeds and tomato pieces, yum!
Heat the chicken stock on high in a stock pot, and then add the mixture from the blender.
Stir in the basil, salt and pepper to taste.
Serve with a great big grilled cheese sandwich for dipping—after all, you have plenty of cheese left over right?
