Gather all the ingredients. If doubling the recipe, please cook one batch at a time in the pan.
Mince ½ onion finely. Lay the cut onion flat side down on the cutting board. With the knife tip pointing toward the root end, make ⅛-inch vertical slices to within ½ inch of the root end. With the knife edge toward the root end, make ⅛-inch horizontal slices, again keeping the root intact. Finally, make perpendicular cuts down through the vertical slices you made.
Heat a large pan over medium heat. When the pan is hot, add 1 Tbsp neutral oil. Then, add the onions. Sauté the onions until tender and almost translucent. Transfer to a large bowl and let it cool.
Once the onions are cool, add ¾ lb ground beef and pork combination to the bowl. Add ½ tsp Diamond Crystal kosher salt, freshly ground black pepper as you like, and ½ tsp nutmeg.
Add the ⅓ cup panko, 2 Tbsp milk, and 1 large egg.
Start mixing it all together with a silicone spatula or spoon. Then, switch to mixing by hand and knead the mixture until it‘s sticky and pale.
Divide the mixture into 4 portions (4 oz, 113 g each) or 6 smaller portions. Scoop out one portion. Toss it from one hand to the other repeatedly about five times to release any air inside the mixture.
Make an oval-shaped patty and place on a tray or plate. Repeat with the remaining portions. Cover the patties with plastic wrap and keep them in the refrigerator for at least 30 minutes before cooking.
Heat a large pan over medium heat. When the pan is hot, add 1 Tbsp neutral oil. Place the patties gently into the pan. Indent the center of each patty with two fingers.
Cook the patties until browned on the bottom side, about 3 minutes. Then, carefully flip and cook for another 3 minutes until browned.
Add 3 Tbsp red wine and reduce the heat to low. Cover the pan with a lid and cook for 5–7 minutes to thoroughly cook the inside of the patties.
Uncover and check that it‘s fully cooked by inserting a skewer; if clear juice comes out, it‘s done. Increase the heat to medium to let the alcohol finish evaporating.
Transfer the hamburger steaks to individual plates. Do not wash the pan as you will make the sauce next using the pan juices.
To the same frying pan, add 1 Tbsp unsalted butter, 3 Tbsp ketchup, and 3 Tbsp tonkatsu sauce. Add 3 Tbsp red wine and 3 Tbsp water to the pan.
Mix well together and bring the sauce to a simmer over medium heat; let the alcohol evaporate.
When the sauce thickens, remove from the heat. Drizzle some sauce over the hamburger steaks.
Pour the remaining sauce into a small bowl or jar and bring it to the table for serving.
