Preheat a skillet over medium heat and add the vegetable oil, allowing it to warm until shimmering.
In a mixing bowl, combine the ground beef, breadcrumbs, egg, minced garlic, thyme, salt, and pepper. Mix gently until just combined—overmixing can make the patties tough.
Form the mixture into four evenly-sized oval or round patties, about 1 inch thick, shaping them to hold together well.
Carefully place the patties in the hot skillet, working in batches if necessary, and sear them for 4-5 minutes per side until golden brown and cooked through. They should have a nice crust and firm texture.
Remove the browned patties and set them aside on a plate. In the same skillet, add the sliced mushrooms and sauté for about 5 minutes, until they release moisture and turn golden.
Pour in the beef broth, scraping up any browned bits from the bottom of the pan, and bring to a gentle simmer. Let it cook for 5 minutes, allowing flavors to meld.
In a small bowl, whisk together flour and a splash of water to make a slurry, then stir it into the simmering gravy. Continue stirring until the gravy thickens slightly and develops a glossy appearance.
Return the seared patties to the skillet, nestling them into the gravy. Cover and simmer for another 10 minutes, until the patties are tender and the sauce is rich and thickened.
Taste the gravy and adjust seasoning with salt and pepper if needed. The sauce should be flavorful and velvety, clinging to the meat and mushrooms.
Serve the Salisbury steak hot, spooned generously with the mushroom gravy over mashed potatoes, rice, or buttered bread for a classic presentation.
