Peel half the skin from the eggplant and cut into bite-size pieces. Salt and drain on kitchen towels for 30 minutes.
Preheat oven to 375°F.
Char the peppers under a hot broiler or over an open flame on a gas stovetop. Place charred peppers in a bowl and cover until cool. Peel peppers, then make a slit lengthwise down one side to carefully remove seeds and ribs.
Heat a large skillet over medium-high heat with EVOO, 4 turns of the pan. Add anchovies and melt them into the oil; add eggplant and cook to light golden, 7-8 minutes. Add garlic, chili paste or flakes, and capers, toss 2 minutes more, then add tomatoes and oregano and toss another 2 minutes. Remove from heat and let cool to room temp. Add the basil and ricotta salata.
Fill peppers with the eggplant mixture, mounding them up a bit. Arrange in a casserole dish.
Combine breadcrumbs, grated cheese and parsley in a small bowl. Moisten with 2 tablespoons EVOO. Top peppers with breadcrumbs then transfer to oven. Cook 20-30 minutes and serve.
Sicilian Roast Stuffed Eggplant