Turn oven on to broil.
Cover a baking sheet with foil and place the red pepper halves on the sheet, inside facing down.
Broil for 10-15 minutes, until outside skin is blackened.
Remove peppers from baking sheet and place in a gallon-sized ziplock bag for 10 minutes, seal.
While peppers are steaming, in a large skillet cook the onion in the olive oil until onions are soft.
Remove peppers from bag, peel off the skin (it should come off easily with your fingers), and chop the peppers.
Add the peppers and garlic to the onion.
Place mixture into a blender or food processor and blend until smooth.
Melt the butter in the same skillet and then add the blended mixture.
Add broth, milk, half and half, and cream cheese. Whisk until smooth and combined.
Let simmer until the mixture thickens (about 3-4 minutes).
Add parmesan cheese, basil, salt and red pepper flakes. Whisk until combined.
Serve sauce over cooked pasta and garnish with fresh basil and parmesan cheese.