Heat olive oil over medium on the stove. Saute onions until soft and translucent.
Mix together in a bowl with beef, bread crumbs, egg, beef broth, dried garlic, salt and pepper. Form into patties and brown both sides in the same pan the onions were cooked, about two minutes each side. Place into bottom of slow cooker and cover with mushrooms.
Whisk together all the remaining ingredients, except the butter and flour, and pour over the patties.
Cook on low for 5 hours or high for 2 ½ hours. Whisk together the butter and flour. Remove the patties from the slow cooker and add the roux. Whisk into sauce to thicken it, then return patties.