Meanwhile, toss together the pork, melted butter, olive oil, salt, and paprika. Refrigerate for 1 hour to marinate.
Preheat the oven to 350˚F (180˚C). Grease a 21- by 15-inch (53 by 38 centimeter) baking sheet with olive oil.
Place the dough on a clean work surface. Roll the dough into a rectangle 1/4-inch (6 mm) thick, and about 2 inches (5 centimeter) larger than your baking sheet. Carefully transfer the dough to the baking sheet.
Fold the edges of the dough over to create a border around the perimeter of the baking sheet.
Spread the meat over the dough in a single layer.
Brush the edges of the dough with the whisked eggs and set the remaining eggs aside.
Bake the pie for 20 minutes. Remove from the oven and pour the remaining eggs over the meat.
Return to the oven and bake for an additional 7 to 10 minutes, until the eggs are cooked and the dough is golden brown.