In a large sauté pan, heat the oil with 1 tablespoon of butter. When the butter has melted, add the onions and caramelize them slowly over medium heat. As always, just like unloading the dishwasher, it seems like it takes hours to caramelize the onions, but be patient.
While the onions are gently sizzling away combine the milk and bread crumbs in a large mixing bowl. All your ground meats are going into this bowl, so make sure it is large. Let the bread crumbs absorb the milk.
Add the ground meats to the bowl along with a teaspoon of salt, black pepper to taste, and the eggs. Mix it well with your just washed hands, making sure to really work everything together so you get a nice blend.
Once the onions are French onion soup brown, remove them from the pan to a plate. Clean the pan and place it back onto the stove but not on the heat. Let the onions cool a minute, then add 3/4 of the onions to the steak mix and knead them in. Form six 6-ounce patties.
Place the pan back onto the heat and turn it to medium high. Add the remaining butter and let it melt and bubble. Once the bubbles begin to subside, add the burgers (if your sauté pan isn't big enough, do this in batches.) Brown them on both sides, cook them to your desired temperature and then gently remove them to a plate while you make the pan gravy.
If your butter is burnt, start over by pouring it out and adding more, but if it is a nice brown butter you did good. Add the remaining onions and your flour of choice and let them cook for a minute or two while you are stirring it around. Add the curry powder, stir once or twice to break out the spice flavors, and then add the water, ketchup, sake, and soy, stirring the entire time until the sauce comes to a boil and thickens. Make sure to use your wooden spoon to scrape up all the goodies from the bottom of the pan. Taste and adjust the seasoning by either adding more soy or salt depending on what you think it needs. If it is too thick, add water a 1/4 cup at a time, stirring between additions. Taste and adjust the seasonings if needed.
Place the chop steaks back into the pan to rewarm them. Serve with steamed white rice and vegetables (traditionally broccoli, potatoes, and sliced tomatoes).