Cut off top 1/2 inch of peppers and reserve. Scoop seeds from cavities. Discard stems and chop pepper tops.
Heat oil in heavy large skillet over medium-high heat.
Add onions, parsley, garlic, and chopped pepper pieces. Sauté until onions soften, about 8 minutes.
Transfer to large bowl. Mix in rice, paprika, salt, pepper, and allspice, and allow to cool for 10 minutes.
Mix in 1/2 cup tomato sauce, then beef and egg.
Fill pepper cavities with beef mixture. Stand filled peppers in single layer in heavy large pot.
Pour remaining 2 cups tomato sauce around peppers. Bring sauce to boil over medium-high heat. Reduce heat to medium-low, cover pot and simmer 20 minutes. Spoon some sauce over each pepper.
Cover; cook until peppers are tender and filling is cooked through and firm, about 20 minutes.
Can be made 1 day ahead. Cool, cover and chill. Rewarm covered over low heat.