In a medium mixing bowl, combine the ground beef with 2 teaspoons Worcestershire sauce, 1/2 teaspoon garlic powder, salt, and black pepper. Mix thoroughly and form the mixture into four uniform patties, each approximately 1/2-inch thick.

In a large skillet over medium-high heat, warm the olive oil. Sear the patties until browned on both sides, then remove them from the pan and set aside.

Pierce the potatoes with a fork several times and microwave for 5 minutes to expedite their cooking. Once they are cool enough to handle, chop them into 1 1/2-inch chunks.

Add the sliced onions to the same skillet, season with salt and pepper, and sauté for around 5 minutes until they turn soft and translucent.

Introduce the chopped potatoes and 2 cups of the beef broth into the skillet. Bring the mixture to a gentle simmer and cook for about 5 minutes, or until the potatoes are fork-tender.

In a separate bowl, blend the remaining 1 cup of beef broth with ketchup, remaining Worcestershire sauce, remaining garlic powder, thyme, and cornstarch. Stir this mixture into the skillet and cook, stirring continuously, until the gravy reaches a thickened consistency.

Reduce the heat to low, return the beef patties to the skillet, and allow them to simmer gently until fully heated through. Adjust the seasoning of the gravy with additional salt and pepper as needed.