Place the bell peppers on a baking sheet and broil on the top rack of the oven, using tongs to turn them as each side blackens. Place the blackened peppers in a plastic bag, tied loosely with some air inside, for 15 minutes. Remove the stems and peel the peppers. Discard the cores and seeds. Cut peppers into wide strips.
Add the peppers, tomato paste, mayonnaise, sour cream, vinegar, garlic, and cayenne pepper in the bowl of a food processor. Pulse until almost smooth, 7 or 8 times. Salt to taste, if needed.