In a mixing bowl, combine the ground beef, breadcrumbs, egg, diced onion, minced garlic, kosher salt, black pepper, Worcestershire sauce, and Dijon mustard. Mix gently until just combined.

Divide the mixture into 4 equal portions and shape into patties about 3/4 inch thick. Make a small indent in the center of each patty.

Heat a large skillet over medium-high heat for about 2 minutes.

Sear the patties in the hot skillet for 4 to 5 minutes without moving them, until deeply browned on the bottom.

Flip the patties and cook for another 4 to 5 minutes, until the internal temperature reaches 160 degrees Fahrenheit. Transfer to a plate and tent loosely with foil.

Add the butter to the same skillet over medium heat. Add the mushrooms and sliced onion and cook for 5 to 6 minutes, stirring occasionally, until softened and lightly caramelized.

Stir in the minced garlic and cook for 30 seconds. Add the tomato paste and Worcestershire sauce and cook for about 1 minute, stirring constantly.

Pour in the beef broth and add the thyme sprigs, scraping up any browned bits from the pan.

Bring the gravy to a simmer. Whisk the cornstarch and water together, then stir the slurry into the simmering gravy. Cook for 1 to 2 minutes until slightly thickened, then season with salt and pepper.

Return the patties to the gravy, reduce the heat to low, and simmer for 2 to 3 minutes. Remove the thyme sprigs and serve immediately.