Heat oven to 425 degrees. In small bowl, combine za’atar seasoning and 2 tablespoons olive oil.
Spread about 1 tablespoon za’atar mixture on each flatbread. Arrange flatbreads on large baking sheet; set aside.
In 10-inch skillet over medium heat, heat remaining olive oil. Cook onion 4-5 minutes, stirring occasionally. Add veal and cook 4-5 minutes until no longer pink, stirring to break up meat.
Remove skillet from heat; stir in feta cheese. Spoon 1/4 of the veal mixture onto each flatbread. Sprinkle each with tomato. Bake 8-10 minutes, or until hot. Sprinkle each flatbread with parsley.