Preheat oven to 375 degrees. Lightly oil a large, deep baking dish.
Cook farro in salted boiling water until tender but still al dente. (This can take 30 minutes or so. Alternately, place farro and 3 cups water in an Instant Pot or electric pressure cooker and cook on high 10 minutes.) Drain in a colander and run under cool tap water. Drain again.
While the farro is cooking, remove the tops from the green bell peppers and carefully hollow them out. If necessary, shave a little off the bottom so they stand level. Reserve the tops of the peppers, pull out the stem and coarsely chop the remainder.
Rub with 1 tablespoon olive oil, then place upside down on a baking sheet. Bake for 15 minutes. Let cool. The peppers will release some of their water during this process. Drain off and discard the excess liquid.
Meanwhile, heat the remaining olive oil in a skillet or saute pan over medium-high heat. Add the onion, celery, and chopped green bell pepper tops. Reduce heat to medium and cook for 10-12 minutes, or until vegetables are tender.
Add the garlic, diced tomatoes, tomato sauce, broth, basil, Italian seasoning, crushed red pepper flakes and Worcestershire sauce. Bring to a simmer and cook for 5 minutes to meld the flavors and thicken the sauce. Let cool slightly. Taste and add a pinch or two of sugar if needed.
Transfer 1 cup of the sauce to a bowl. Add beef, egg, Parmesan cheese, 1 cup of Mozzarella, salt, black pepper, cooked farro, and half the parsley. Stir to combine.
Spread 1 cup of the sauce over the bottom of the dish.
Fill each pepper with equal amounts of the beef-farro combination and place upright in baking dish. Pour the remaining sauce over each pepper.
Cover with aluminum foil. Bake for 50-60 minutes or until an instant-read thermometer inserted into each pepper registers 160 degrees.
Top with remaining cheese and return to the oven for 5-10 minutes or until cheese is nicely melted and the peppers are at 165 degrees.
Garnish with remaining chopped fresh parsley.