Preheat broiler. Cut peppers in half and remove seeds. Lightly coat the peppers with olive oil and place cut side down on cookie sheet. Place under broiler until skin is blackened and softened. Place in a paper bag an alllow to steam for about 5-10 minutes.
Remove the skin from the peppers and cut into small pieces.
In a frying pan saute the garlic, sliced basil, red peppers and onion in olive oil. Cook for 10 minutes.
Mix corn starch and half and half together well, no lumps.
Place mixture into blender (be careful it will be hot, leave the lid of blender slightly askew but not enough so that it will spray out) Mix to desired consistency.
Put mixture back in frying pan and heat to a boil. Add in half and half to the desired consistency.
Add in cheese and cook until cheese melts. Stir in butter. Season to taste with salt and pepper. Simmer for 5 minutes. If it thickens too much add some additional half and half.