Preheat oven to 300°F.
Use a meat mallet to tenderize the meat by pounding to ½-inch thickness.
Heat 1 tablespoon of olive oil in a Dutch oven or deep braising skillet over medium-high heat. Working in batches, if necessary, add the steak and cook until browned, about 5 minutes per side. Remove from the pan and set aside.
Reduce the heat to medium; add the butter to the drippings in the pan. When the butter melts, stir in the mushrooms and onion; cook until starting to soften, about 5 minutes. Add the garlic and cook until fragrant, about 30 seconds. Stir in the broth and Worcestershire sauce, scraping up any browned bits from the bottom of the pan with a wooden spoon.
Return the steaks and any juices to the pan. Sprinkle dry onion soup mix over all. Tuck thyme and rosemary sprigs into the broth.
Cover and bake for 2 ½ - 3 hours, or until the meat is tender. Check the steaks once or twice during the cooking process, adding more broth to the pan if necessary. You want about ½ - ⅓ of the steaks submerged in the liquid for proper braising. If the steaks are still tough at the end of the cooking time, return the pan to the oven and continue baking.
Remove the meat from the pan and cover loosely with foil to keep warm. Discard the herb sprigs.
To thicken the gravy, bring the liquid to a boil over medium-high heat. If you’d like even more gravy in your pan, you can add more beef broth at this time. Add about half of the cornstarch slurry, whisking until the mixture thickens. If you’d like a thicker gravy, add the remaining cornstarch slurry (I find that I don’t usually need all of the cornstarch). To thin the gravy, add extra broth. Taste and season with salt and pepper, if necessary.
Slice the steaks thinly against the grain. Spoon the gravy over top and serve with mashed potatoes, noodles or rice. Garnish with chopped fresh herbs.