Heat up 1 tbsp olive oil over medium-high heat in a pan. Add in the onion and mushrooms. Season with a little salt and pepper, and cook until the onion is translucent. Place in a bowl and let cool completely.
In a large bowl, combine together the ground beef, ground pork, salt, black pepper, panko breadcrumbs, milk, egg, and the onion mushroom mixture.
Form into even patties. Slightly flatten the patty and place a cheese cube inside. Close up the patty by pushing the meat to the top to seal it up. Make sure the cheese is not visible or else it will leak out when cooking. Then, gently shape it to a circular form.
Rest the patties in the fridge for 30 minutes to help keep its shape and to prevent the fat from melting quickly when it cooks.
In a pan over medium-high heat, add in the remaining 1 tbsp of olive oil. Once the oil is heated, cook the patties for 3-4 minutes on each side. Then add in the red wine and cover to let it steam for 6-8 minutes. Remove from the pan.