Preheat the oven to 425° F.
Place the peppers in a roasting pan and roast, turning every 15 minutes, for 45 minutes, until the skins are wrinkled and lightly charred.
Transfer the peppers to a cooling rack. When cool enough to handle, peel the peppers over a bowl, allowing the juices to collect in the bowl. Discard the skins. Combine the peppers, collected juices, and balsamic vinegar in a food processor and process until smooth. Season with salt.
The coulis will keep, tightly covered, in the refrigerator for up to 3 days.
For a finer sauce, strain the purée through a strainer, pushing it with a wooden spoon.