Preheat An Outdoor Grill For Medium Heat, And Lightly Oil The Grate. Knead Together The Ground Beef, Worcestershire Sauce, Parsley, Salt, And Pepper In A Bowl. Form The Mixture Into 8 Equal-Sized Balls; Flatten To Make 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 Center. Cook On The Preheated Grill Until The Burgers Are Cooked To Your Desired Degree Of Doneness, 7 To 8 Minutes Per Side For Well Done. An Instant-Read Thermometer Inserted Into The Center Should Read 160 Degrees F (70 Degrees C).