In a large bowl, mix bread crumbs, Parmesan, parsley, and onion. Add eggs, salt, pepper, 3/4 cup ketchup, beef, veal and pork, and combine thoroughly until evenly mixed, using your hands if necessary. Form into a loaf in a baking pan and brush top with 1 tablespoon ketchup. Bake in the oven for 50 minutes to 1 hour and let rest 10 minutes before slicing.
About 10 to 20 minutes before the meatloaf is done, begin the sauce. Melt half of the butter in a saute pan (reserving the other 1/4 cup) over medium-high heat, and saute onion until it caramelizes. Add the mushrooms and cook until they become tender and give up their juices. Strain and set aside. In another saucepan, whisk together demi-glace, tomato paste, and red wine and simmer over low heat, allowing to reduce and thicken. Just before serving sauce, whisk in the remaining 1/4 cup of cubed butter, and add mushrooms. Taste and add salt and pepper, as needed.
Slice meatloaf and transfer to a serving dish. Spoon sauce over and serve additional sauce on the side.