In a blender, combine the red peppers, broth, vinegar, and oil and process until smooth. Transfer mixture to a small saucepan and set over medium heat. Bring to a simmer, partially cover, and simmer for 10 minutes. Remove from the heat and stir in the basil. Season, to taste, with salt and pepper. Let come to room temperature and store in a plastic container in the refrigerator for up to 1 week or in the freezer up to 3 months.