New-fangled stuffed peppers

8 large red and/or yellow bell peppers or other large sweet variety;
8 ounces tuna packed in olive oil, preferably fillets in a jar;
2 tablespoons raisins or currants, soaked in hot water for 10 minutes, then drained;
1 cup large fresh bread crumbs from very crusty bread;
1⁄4 cup ripe black olives, such as Kalamata, pitted and chopped;
3 tablespoons pine nuts, toasted;
3 tablespoons chopped fresh basil;
3 tablespoons chopped flat-leaf parsley;
2 tablespoons capers, drained;
2 garlic cloves, finely chopped;
2 teaspoons finely grated orange zest;
1 tablespoon fresh orange juice;
1⁄2 teaspoon kosher salt, or to taste;
1⁄4 teaspoon ground black pepper, or to taste;
Extra-virgin olive oil, as needed;
1⁄4 cup coarsely grated Asiago, Pecorino, or Parmesan cheese.

Preheat the oven to 350°F.
Roast the peppers. When the peppers are cool enough to handle, carefully remove the stems. Make a long slit down one side of each pepper and open like a book. Remove the seeds and arrange the peppers in a single layer on a work surface.
Drain the oil from the tuna into a small bowl and set it aside. Place the tuna in a large bowl and fold in the raisins, bread crumbs, olives, pine nuts, basil, parsley, capers, garlic, orange zest, and orange juice and 3 tablespoons of the reserved tuna oil. Season with the salt and pepper.
Divide the filling among the peppers. Fold the peppers closed or roll them up to enclose the filling, depending on their shape. Place the peppers in a 9 × 13-inch glass or ceramic baking dish. Drizzle the remaining 3 tablespoons of tuna oil over the tops. If there is not enough tuna oil, make up the difference with olive oil. Sprinkle with cheese and bake until the cheese melts and the filling is warm, about 15 minutes. Serve warm or let cool to room temperature.
Make-ahead note: You can fill the peppers up to 1 day ahead. Store covered and refrigerated. Increase the baking time by about 5 minutes.