In a large mixing bowl, combine ground beef, finely diced onion, egg, Worcestershire sauce, garlic powder, thyme, salt, and pepper. Gently mix with your hands until just combined - do not overmix. Divide into 4 equal portions and shape into oval patties about 3/4-inch thick.

Heat olive oil in a large skillet over medium-high heat. Add the patties and sear for 4-5 minutes per side, until deeply browned. The patties will not be fully cooked through. Remove and set aside on a plate.

Reduce heat to medium and add butter to the same skillet. Add sliced mushrooms and diced onion, sautéing for 5-7 minutes until softened and golden. Add minced garlic and cook for 1 minute more.

Sprinkle flour over the vegetables and stir constantly for 1 minute to cook out the raw flour taste. This creates the roux for thickening.

Gradually whisk in beef broth, scraping up all the browned bits from the bottom of the pan. Stir in soy sauce and additional Worcestershire sauce. Bring to a simmer and cook until slightly thickened, 3-4 minutes.

Return the seared patties to the skillet, nestling them into the gravy. Reduce heat to low, cover, and simmer for 10-15 minutes, or until patties are cooked through (160°F internal temperature).

Taste the gravy and season with salt and pepper as needed. The gravy should be rich and coat the back of a spoon.

Serve hot over mashed potatoes, egg noodles, or rice, spooning plenty of gravy over the top.