Although it's very tempting to buy a pre-jarred marinated pepper, there's nothing that tastes as good as one that you char in your own fireplace, and marinade with carefully-chosen olive oil. Prepared with care, this dish will never disappoint.
Prepare a hot fire in a gas or charcoal grill or preheat a grill pan or heavy-bottomed skillet over high heat. Place the peppers on the grill or in the grill pan or skillet, and cook them, turning frequently, until they are charred on all sides and the flesh is tender, 15 to 20 minutes. (Alternatively, you can cook the peppers over the direct flame of a gas stove.)
Place the peppers in a plastic bag or a large bowl. Close the bag or seal the bowl tightly with plastic wrap and set the peppers aside to steam until they are cool enough to handle. Rub off the charred skin, but do not rinse them with water. De-stem and open up the peppers and slide off the core and seeds.
Rip the peppers into big strips and layer them in a 1-quart (1L) canning jar. Scatter the garlic slices and basil leaves between each layer and pour some marinade made with the olive oil, vinegar, anchovies, capers and salt on each layer.
Set the peppers aside to marinate for at least 20 minutes, or until you are ready to serve them. Store with the jar lid on, refrigerated for up to several days. Bring the peppers to room temperature before serving.