Heat the oven to 475°F with a large rimmed sheet pan inside. Divide the dough into four pieces and roll each on the measured flour into an oval about 8 by 4 inches.
Mix the beef, onion, tomato, pepper, parsley, tomato paste, paprika, salt and black pepper until evenly combined.
Set the dough ovals on parchment and spread a quarter of the filling over each, leaving a 1/2-inch border and keeping the beef layer under 1/4 inch thick. Fold the long edges slightly inward and pinch each end to make a boat.
Brush the exposed dough with olive oil. Carefully slide the parchment onto the hot sheet pan and bake for 12 to 15 minutes, until the crust bottoms are browned and the beef centers reach 160°F.
Rest for 2 minutes, then serve one pide per person, cutting crosswise if desired.