Sauté: In a stock pot or large skillet, sauté the tomatoes and onion in olive oil over high heat until the onions are translucent.

Melt: Add the feta, cheddar, and thyme. Season with salt and pepper. Cook until the tomatoes break open and the juices meld with the melted cheeses, about 5 minutes.

Blend: Working in batches, add the tomato juice and the tomato-cheese mixture to a blender. Puree until smooth. (For a more rustic, textured soup, pulse the blender only a few times instead of pureeing).

Simmer: In a clean stock pot, heat the chicken stock on high, then add the blended tomato mixture.

Finish: Stir in the fresh chopped basil and add final salt and pepper to taste. Serve hot, preferably with a grilled cheese sandwich for dipping.