In a large frying pan, heat 2 teaspoons of olive oil, add the meat, black pepper, and 2 tablespoons of soy sauce, cook for about 2 minutes, until the meat turns pink. Transfer the contents of the skillet to a bowl and cover to keep the meat warm.
Pour the remaining oil into the pan, add the onion and garlic, cook for about 1 minute. Place the bell peppers in a skillet, add the wine and the remaining soy sauce, and bring to a boil. Put the meat in a skillet and simmer for about 5 minutes.
Put mayonnaise sauce on pita bread, sprinkle with torn lettuce leaves, tomatoes, and green onions. Put 3/4 cup of meat filling on each sheet of pita bread and roll into a roll.