Roast your red pepper (unless you've simply bought roasted red peppers already). Remove the stem, inside veins, and seeds from the bell pepper. Cut in fourths. Rub a little olive oil over a baking pan and place the peppers on the pan, cut side down. Cook under the broiler until the skins become charred looking, about 6-8 minutes for me. I find that broilers are all a little different, so keep an eye on them so they don’t burn.
Once you remove them from the oven, place in a plastic bag (or reusable bag of some kind). Seal and let them steam for a couple of minutes. Once they are just cool enough to handle, remove the bags and peel off the skins.
Go ahead and begin boiling water for your pasta now.
Finely chop the roasted pepper, onion, and mince the garlic. In a large sauce pan, add the butter and olive oil over medium heat. Cook the onion for 2-3 minutes until it softens well. Then add the roasted pepper, garlic, and red pepper flakes. Cook for another 3-4 minutes. Then add the vodka and cook for about 30 seconds, then stir in the tomato paste.
Then stir in the cream and cheese. The mixture will be pretty thick at this point. Once the pasta has cooked, reserve 1 cup of the pasta water and add it to the sauce.
Serve over the warm pasta with some chopped basil.
You can store this sauce for up to a week in a seal container in the refrigerator. If you plan to store it longer, I would recommend freezing the sauce.