Preheat an barbecue for medium heat and lightly oil the grate.
Knead together the beef mince, Worcestershire sauce, parsley, salt and pepper in a bowl. Form the mixture into 8 equal-sized balls; flatten to make very thin patties. Place about 1/4 cup of feta cheese onto each of four of the patties. Top each of the patties with cheese with one of the patties without; press the edges together to seal the cheese into the centre.
Cook on the preheated barbecue until the burgers are cooked to your desired degree of doneness, 7 to 8 minutes per side for well done.