Preheat oven to 375ºF (190ºC) and prepare parchment-lined baking sheet.
Arrange peppers and tomatoes on baking sheet and drizzle with 1 tablespoon olive oil. Roast for 30 minutes then turn the peppers with tongs and continue roasting for another 20 minutes. Add walnuts and garlic and continue to roast until the walnuts are toasted and fragrant and the peppers have softened, and their skins are wrinkled and charred, about 10 minutes. Remove from oven and let cool to room temperature.
Remove garlic peels and transfer peppers, tomatoes, garlic and walnuts to the bowl of a food processor. If you have a smaller food processor, proceed in batches until reduced. Add vinegar, salt, pepper, paprika and cayenne and process on high until smooth. Add remaining 2 tablespoons of olive oil and continue to blend until well combined.
Transfer to a sealed container and store for up to 5 days in the refrigerator. If serving immediately, transfer to a sauce pan and reheat before serving.