In the bowl of a food processor fitted with a metal blade, combine bell pepper, onion, and 1/2 teaspoon salt. Process, scraping down sides of bowl as needed, until finely chopped, 10 to 20 seconds. Transfer mixture to a fine-mesh strainer set over a medium bowl and let drain for at least 10 minutes.
Press on onion-pepper mixture to extract any remaining liquid, then return to food processor bowl; discard drained liquid. Add parsley, pepper paste, tomato paste, garlic, allspice, paprika, cumin, pepper, and remaining 3/4 teaspoon salt. Process, scraping down sides of bowl as needed, until mixture is finely chopped.
Using your hands, break ground meat into walnut-sized chunks and distribute around bowl. Process, scraping down sides of bowl as needed, until mixture is just combined, 5 to 10 pulses. Set aside while you roll out dough. If you refrigerate this mixture, let sit at room temp for 30 minutes before you make the breads.