**Prepare the Beef:**
- In a large skillet or griddle, heat over medium-high.
- Add the ground chuck, breaking it apart with a spatula.
- Season with salt, pepper, and garlic powder.
- Cook for 8-10 minutes, stirring occasionally, until browned and cooked through.
**Melt the Cheese:**
- Reduce heat to medium.
- Place cheese slices over the beef and let it melt, about 1-2 minutes.
**Toast the Hoagie Rolls:**
- While the beef cooks, slice hoagie rolls and toast them on a dry pan until golden brown.
**Prepare the Au Jus (Optional):**
- In a small saucepan, combine beef broth, Worcestershire sauce, garlic powder, and thyme.
- Simmer for 10 minutes to concentrate flavors.
**Assemble the Sandwich:**
- Layer shredded lettuce and sliced tomato on the toasted hoagie rolls.
- Add the cheesy chopped beef mixture.
- Serve immediately with au jus on the side for dipping.