In a large skillet, heat olive oil over low to medium heat. Add onions and cook until slightly fragrant and slightly translucent. Add garlic and sauté for another half minute. Add peppers and peas and cook for another 1-2 minutes until softened. Remove from pan and set aside. Add ground beef, spices, parsley, salt and pepper to pan and stir to combine, Sauté until ground beef is brown and cooked through. Using end of a wooden spatula, chop up ground beef into small pieces as it cooks. Return onion mixture to pan and stir to combine all ingredients. Remove from pan into a large bowl. Allow to cool slightly. Add the shredded Parmesan cheese to mixture while it is still warm and stir. Set aside.
Preheat oven to 400°F.
Lightly flour a clean work surface. Then, using a rolling pin, roll out one sheet of thawed puff pastry dough to about 1/8-inch thickness. Using a football shaped cookie cutter (we used a 4-inch size), cut as many footballs from the dough as possible. Place half of the football shapes onto a parchment-lined baking sheet for the football bottoms.
Using a sharp knife score the top pieces about 1 inch from one long edge with a long arc. Try not to cut all the way through dough. Next add short “stitch” cuts perpendicular to the original cut for football laces.
Using a tablespoon, scoop a portion of the beef mixture onto each football shape, leaving a ½ inch border all around the edge. Sprinkle more shredded parmesan atop each scoop.
Use a pastry brush or your finger to moisten the border edge of the bottom football shapes with the beaten egg. Then, place the top dough piece aligned over each bottom piece. Using the tines of a fork, crimp edges of dough together all around the football shape to form sealed pockets.
Brush each football with remaining egg. Bake for approximately 15-20 minutes until shapes have puffed and are golden brown.
Serve immediately.