In a bowl, mix the minced meat with salt, pepper, and the egg. Grate the feta cheese and mix it into the minced meat.
Coat each bread slice with approximately 0.5 cm thick layer of the minced meat mixture, ensuring it reaches into the corners. Press the mixture firmly with a spoon or fork.
Grill the minced meat side on medium-high heat until the pork is cooked through (internal temperature 63°C / 145°F). Turn and grill the bread side until golden brown.
Serve with ketchup, barbecue sauce, or other condiments of your choice.