In a large skillet melt the butter and sautee the minced onion until translucent. Combine rest of the ingredients in a large bowl, add the cooked onion and mix well. Form the mixture into 6 oval-shaped patties.
In the same large skillet, heat 2 tablespoons of olive oil over medium-high heat. Fry the hamburger steak on both sides until they are cooked through and browned. Once they are done, remove the patties from the skillet cover and set them aside.
For the mushroom gravy
Sautee the onion in the 1 Tbsp butter in the same skillet until it becomes translucent.
Add 2 minced garlic cloves and 8 ounces of sliced mushrooms. Cook the mixture for several minutes until the mushrooms are tender.
Add 3 tablespoons of flour and toss to coat. Slowly add 3 cups of beef broth, stirring constantly. Add 2 tablespoons of Worcestershire sauce, 1 teaspoon of basil, and salt and pepper to taste. Bring the mixture to a boil, then reduce the heat and let it simmer for 5-10 minutes until the gravy has thickened.
Add your hamburger steaks to the gravy and heat through.