In a large skillet over medium-high heat, cook the bacon until most of the fat is rendered but it is not yet crisp. Transfer the bacon to the bowl of a food processor and set aside. Remove all but 3 tablespoons of the bacon fat from the skillet. Reserve the additional rendered bacon fat in a small bowl and set aside.
Add the chopped onions to the fat in the pan and cook, stirring occasionally, until very soft and caramelized around the edges, about 6 minutes. Combine the onions with the bacon in the bowl of the food processor and process until smooth. Transfer to a large bowl and set aside to cool.
Heat 3 tablespoons of the remaining bacon fat in the pan. Add the mushrooms and 1 teaspoon of the salt, and cook, stirring occasionally, until they have released their liquid and are golden brown around the edges, about 5 minutes. Add the minced shallots, thyme, and rosemary, and cook until the shallots are soft, about 2 minutes. Add the red wine and cook until almost completely evaporated. Sprinkle the flour over the shallots and mushrooms, and stir to combine. Cook for 1 minute. Add the beef stock and cook for 5 minutes, until thickened. Add 1/2 cup of the heavy cream, stir to combine, and cook until the sauce is thick enough to coat the back of a spoon and the flavors come together, about 6 minutes. Cover and keep hot while you prepare the meat patties.
Preheat the broiler to 500 degrees F.
In the mixing bowl with the pureed onion-bacon mixture, add the beef, veal, pork, remaining 2 tablespoons of heavy cream, egg yolks, mustard, Worcestershire Sauce, garlic, remaining 1 1/2 teaspoons of salt, and pepper, and mix lightly but thoroughly.
Shape into 6 oval patties, about 1 cup each, and 1-inch thick, and transfer to a nonstick baking sheet or broiling pan. Broil the patties close to the heat source, about 4 minutes on each side for medium-rare.
Add the meat pan drippings, butter, and chives to the sauce and stir until the butter is thoroughly incorporated. Taste and adjust the seasoning if necessary.
Serve the patties immediately with the Roast Garlic Mashed Potatoes, with some of the mushroom sauce ladled over the top.
Yield: 6 generous servings