Preheat oven to 375°F. Grease a 9x13-inch baking dish and set aside.

In a large skillet over medium-high heat, cook the ground beef and diced onion together, breaking meat apart as it cooks, until fully browned and onion is softened, about 7 to 8 minutes. Drain excess fat and return skillet to heat.

Add sliced mushrooms to the skillet in a single layer. Cook undisturbed for 3 to 4 minutes to develop browning, working in batches if needed to avoid crowding. Continue cooking for 2 to 3 more minutes, then add garlic and stir for 1 minute until fragrant.

In a medium bowl, whisk together the cream of mushroom soup, sour cream, beef broth, Worcestershire sauce, dried thyme, salt, and pepper until smooth.

Pour the sauce over the beef and mushroom mixture in the skillet. Stir to coat everything evenly.

Transfer the mixture to the prepared baking dish and spread into an even layer. Sprinkle shredded cheese evenly over the top. Add breadcrumbs or crushed crackers over the cheese if using.

Bake uncovered for 20 to 25 minutes until the sauce is bubbling at the edges and the cheese is fully melted with light browning beginning at the edges. For a deeper golden top, broil for the final 2 minutes.

Remove from oven and let rest for 5 minutes before scooping to allow the sauce to set.