- Cut the tomatoes in half and place on a foil covered baking sheet, cut side down. Move an oven rack to the highest position and turn on the boiler. Broil 5 to 15 minutes, until the tomato skins are blackened. Move the pan around every few minutes to ensure equal roasting. 
- Remove from oven and cover with foil, letting the tomatoes cool and steam for 10 minutes. Remove the skins from the tomatoes and transfer to a high speed blender. 
- Melt the butter in a frying pan and sauté the onions, garlic, oregano, salt, pepper, and crushed red pepper for about 5 minutes or until the onions are translucent. 
- Add to a blender along with basil leaves, yogurt, broth, and shredded cheddar cheese. Blend on high until smooth (if using all fresh tomatoes, you might have to do this in batches). 
- Pour into a large pot and simmer for 10 to 15 minutes on medium-low heat. Add more salt to taste.