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In a skillet over medium heat, heat oil. Add mushrooms and cook, stirring regularly, for about 1 to 2 minutes. With a slotted spoon, remove from pan and keep warm.
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Add beef patties in a single layer and cook for about 1 to 2 minutes on each side or until lightly browned but not cooked through. Remove burgers from pan and drain on paper towels. Keep warm.
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In a saucepan over medium heat, heat the butter until melted. Sprinkle in the flour and whisk until smooth and blended. Continue to cook, stirring regularly, for about 2 to 3 minutes or until roux turns lightly golden.
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Slowly add beef stock, whisk until smooth, and continue to cook until sauce begins to thicken. Add salt and pepper for the gravy.
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Add meat patties in a single layer in the pan. Lower heat, cover, and continue to cook for about 10 to 15 minutes or until meat is fully cooked.
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Add mushrooms during the last 5 minutes and cook until heated through. Serve hot.