How to Make It
Preheat the oven to 400°. In a large skillet, melt 1 tablespoon of the butter in 1 tablespoon of the oil. Add the onion and garlic and season with generous pinches of salt and pepper. Cook over moderate heat, stirring occasionally, until softened, about 5 minutes. Add the mushrooms and thyme and cook, stirring occasionally, until the mushrooms are browned and softened, about 4 minutes. Transfer to a plate. Wipe out the skillet.
Place the flour in a shallow bowl. Season the steaks generously with salt and pepper. Dredge the steaks in the flour and shake off the excess. Transfer the steaks to a plate.
In the same skillet, melt 1 tablespoon of the butter in 1 tablespoon of the oil. Add 2 of the steaks and cook over moderate heat, turning once, until browned, about 2 minutes. Transfer the steaks to a 9-by-13-inch baking dish. Wipe out the skillet. Repeat with the remaining steaks, oil and butter.
Add the broth to the same skillet and bring to a simmer, scraping up the browned bits on the bottom. Cook until the broth reduces by half, about 10 minutes. Whisk in the sour cream and dry mustard. Return the mushrooms to the skillet and cook, stirring, until the mushrooms are coated in the sauce, about 1 minute. Remove the skillet from the heat and season the sauce with salt and pepper. Scrape the mushroom sauce over the steaks.
Cover the baking dish with foil and bake for about 1 hour, until the steaks are tender. Remove from the oven and discard the foil. Garnish the steaks with parsley and serve warm. Pass the mashed potatoes and boiled peas at the table.