In a large bowl, combine the ground beef, panko breadcrumbs, egg, 2 minced garlic cloves, 2 tablespoons ketchup, Dijon mustard, oregano, 1 teaspoon Worcestershire sauce, and salt.
Using your hands, mix all the ingredients really well. Form the mixture into 5 equal oval patties, around 1-inch thick.
In a large nonstick skillet, heat the olive oil over medium heat. Add the steaks; cook on each side for around 1 to 2 minutes, until they brown. You don't have to cook them completely in this step; you just want to develop a nice crust. Once browned, transfer the steaks to a plate and set them aside.
In the same skillet, cook the mushrooms and remaining garlic for 1 to 2 minutes, scraping the bottom of the pan.
Add the butter. Once melted, whisk in the flour and stir constantly for 30 to 40 seconds. Gradually add the beef broth, continuing to whisk.
Continue to whisk in the other ingredients: the water, the remaining Worcestershire sauce, and the remaining ketchup.
Add the partially cooked steaks and their juices back to the skillet and nestle them into the gravy. Cook for around 8 minutes, until they're fully cooked through. You can keep stirring the sauce as it continues to thicken.
Serve the steaks over mashed potatoes or roasted potatoes with some of the mushroom gravy drizzled on top.