Soak the stale bread in warm water for 5 minutes. Peel and wash the onions. Cut the beef and one onion into small pieces and grind through a meat grinder. Squeeze the soaked bread well to remove excess liquid, then add to the ground meat. Season with salt, ground black pepper, and ground coriander to taste. Beat the meat mixture well with your hands until combined.
Finely chop the mushrooms and the second onion. Heat vegetable oil in a pan over medium heat. Add the mushroom-onion mixture and fry for 3-4 minutes until the mushrooms are softened and beginning to brown, stirring occasionally. Add ground black pepper and ground coriander to taste, and adjust salt as needed.
Divide the meat mixture into 13 equal portions.
Take one portion and flatten it between your palms into a thin patty. Place 0.5 teaspoon of the mushroom filling in the center. Fold and shape the meat around the filling to form a sealed patty.
Place the breadcrumbs in a shallow dish. Coat each meat patty thoroughly on all sides with breadcrumbs. Heat vegetable oil in a large pan over medium-high heat until shimmering. Working in batches to avoid crowding, place the coated patties in the pan, cover with a lid, and fry for 2 minutes on the first side. Flip and fry for another 2 minutes on the second side until golden brown and the internal temperature reaches 63 °C (145 °F).
Serve the meat zrazy hot with the remaining mushroom filling, mashed potatoes, or your choice of side dish.