Step 1Heat the oven to 350 degrees. Rub the peppers all over with 2 tablespoons olive oil, season with one-half teaspoon salt, and place on a parchment-lined baking sheet. Roast for about 30 to 40 minutes, turning the peppers occasionally, until their skins are wrinkled and slightly charred.
Step 2Let the peppers cool completely. Slice in half (through the stem end), discard the stem, peel off the skin with your fingers and a paring knife, and slice the halves lengthwise into strips 2 inches wide. Scrape the seeds from the strips, and lay them in a sieve to drain and dry.
Step 3To make the stuffing, drain the tuna and break it into flakes in a medium-size bowl. One at a time, mix the seasonings into the tuna with a fork: chopped anchovies, capers, vinegar, mustard, mayonnaise, parsley, 2 tablespoons olive oil, and about one-half teaspoon salt. Stir vigorously, breaking up lumps of fish, until the stuffing is soft and fairly smooth. Add more of any seasoning to taste. This makes about 1 2/3 cup filling.
Step 4Drop a scant tablespoon of stuffing at one end of each roasted pepper strip and roll it up snugly, creating a neat cylinder. Press the pepper as you wrap, so it adheres to itself and stays closed.
Step 5To serve, arrange all the rolls on a platter, drizzle a bit more olive oil all over, and sprinkle lightly with coarse salt.