Place the pepper on an open gas flame and roast, turning them frequently with tongs, until all sides are charred black, 7 to 10 minutes. (Alternately, the pepper can be roasted under a broiler, or on top of a gas or charcoal grill.) Place the blackened pepper in a plastic or paper bag, and let rest until cool enough to handle, about 15 minutes.
Peel the pepper, remove the seeds and stems, and coarsely chop.
Heat 2 tablespoons of the oil in a small skillet over medium heat. Add the shallots and cook, stirring, for 1 minute. Add the peppers and cook for 4 minutes. Remove from the heat.
Combine the peppers, shallots, cilantro, basil, vinegar, salt, and pepper in the bowl of food processor or blender, and process for 20 seconds. With the machine running, add the remaining oil through the feed tube in a steady stream and process until thick and smooth. Transfer to a container until ready to serve.
Yield: about 1 cup