Preheat oven to 400°. Remove stems from mushrooms and wipe the caps clean a damp paper towel. Rub caps with about ½ tablespoon of olive oil. Arrange, stem sides up, in a roasting pan, oven-safe skillet, or on a baking sheet. Bake 15 minutes, until they tenderize a bit and begin to release their juices.

While mushrooms bake, coat the bottom of a medium skillet with 1 tablespoon of olive oil and place over medium heat. Add onion and sauté until soft and translucent, about 5 minutes. Add garlic and sauté 1 minute more. Add beans to skillet, flip a few times to incorporate, and allow to cook until heated throughout, about 2 minutes. Use a fork or potato masher to lightly mash about half of the beans. Stir in parsley, basil, breadcrumbs and red wine vinegar. Season with salt and pepper to taste.

After portobellos have baked for 15 minutes, remove them from the oven and spread about 2 tablespoons of puttanesca sauce inside of each cap, using a spoon to spread it around a bit. Stuff each cap with a quarter of the bean mixture, pressing firmly. Spoon 3-4 tablespoons more of puttanesca sauce on top of bean mixture. Return portobello caps to the oven and bake 6-8 minutes more, until mushrooms are very tender.

Spoon a bit more puttanesca sauce on onto the bottom half of each roll. Stuff rolls with portobellos, and top with additional puttanesca sauce, if desired. Serve.