Form the beef patties by combining all ingredients in a large mixing bowl. Use your hands to mix the ingredient well, then form the mixture into 4-6 patties, pressing them together firmly.
Heat 2 Tablespoons olive oil in a large skillet over high heat. Fry the patties for 1-2 minutes on each side, until browned, then remove them from the skillet to a plate. Tent with foil to keep them warm. *The patties will finish cooking in the gravy.
To the same skillet, add the onion and garlic for the gravy, along with more oil if needed. Sauté over medium heat until onion is translucent, about 3-5 minutes.
Add the mushrooms and sauté for an additional 3-5 minutes, until tender.
Reduce heat to medium low. Add the butter until melted, then add the flour. Mix together and cook for 2-3 minutes, stirring constantly, to cook off the raw flour taste. Slowly whisk in the broth, then add the remaining ingredients.
Once the gravy begins to bubble, add the steaks back into the pan and cook over medium heat 7-10 minutes. Stir gently around the patties until the gravy is thickened.
Remove from heat and garnish with fresh parsley or thyme. Serve over mashed potatoes or noodles.