In a large bowl, combine the ground beef with the beaten egg, panko crumbs, ketchup, olive oil, rosemary, oregano, salt, and Dijon mustard. Mix it until just combined; avoid overmixing as this could lead to tough patties. Shape the mixture into four equal-sized patties.

Heat a skillet over medium heat and add a little olive oil. Once the oil is hot, add the patties. Cook for about 4-5 minutes on each side until they’re browned and cooked through. Remove them from the skillet and set aside.

In the same skillet, melt butter over medium heat. Add the sliced mushrooms and sauté them until they’re soft and browned. This will take around 5-7 minutes.

Sprinkle the flour and smoked paprika over the mushrooms, and stir continuously. Gradually pour in the beef broth, whisking continuously to remove any lumps.

Finally, add the Worcestershire sauce, ketchup, onion powder, salt, and pepper to taste. Let it simmer for a few minutes until the sauce thickens.

Return the cooked patties to the skillet, spooning the mushroom gravy over them. Allow everything to simmer together for another 2-3 minutes to meld the flavors.

Serve hot with mashed potatoes and roasted broccoli.