Saute half of chopped onion in 1 Tabsp hot oil in medium skillet over medium heat until tender. Add garlic, and saute 30 seconds. Remove from heat and let cool.
Combine cooked onion mixture, beef, and next 4 ingredients, 1/4 teasp salt, and 1/2 teasp pepper. Shape into 6 patties.
Cook patties in remaining 2 Tabsp. hot oil over medium-high heat 3 minutes on each side or until browned. (Do not cook until done). Remove patties and set aside.
Add remaining onion to drippings in skillet, and saute over medium-high heat until tender; add mushrooms and saute 3 minutes. Whisk in flour, and cook, stirring constantly, 1 minute, whisk in wine, broth, and remaining 3/4 teasp salt and 1/2 teasp of pepper. Bring to a boil, reduce heat to low and simmer stirring occasionally, 5 minutes.
Place patties in lightly greased baking dish, top evenly with gravy.
Bake, covered, at 350 for 25 minutes or until done.
In the summer I make this recipe in my electric fry pan.