For the empanada filling: Head a large skillet over medium heat. Add butter and melt. Add onion and cook until softened and translucent. Add tomato paste, garlic, cumin, oregano, and cayenne. Stir thoroughly to combine the cook for about 2 minutes.
Add ground beef and cook until the seasonings mix in and meat is just cooked through. Add beef broth and simmer over low until most of the moisture evaporated and meat just looks wet.
Turn off heat. Stir in cheese, egg, and green onion. Cool filling in the refrigerator.
Meanwhile, roll out pastry dough 1/8th of an inch thick and cut out 5″ circles. When filling is cooled, add about a tablespoon to each circle. fold circle in half and repulge.
When all empanadas are shaped, preheat oven to 425F. Bake them on a lined baking sheet for 20 minutes. if you wish to freeze them, freeze them on a baking sheet, then place in bags. Bake frozen empanadas for 25-30 minutes at 425F.