In a large bowl, combine the turkey, panko, egg, mustard, Worcestershire sauce, salt, pepper, garlic salt and onions. Mix well- but do not compact the mixture or else you will have a tough burger.
Form the mixture into patties. Set aside on a plate.
In a large pan, over medium high heat, add 2 TBSP of oil. Add the turkey patties to the pan and brown on each side for 1 minute. The burgers will not be cooked through. Remove from the pan once browned on both sides. Set aside.
For the sauce- In the same pan, add the remaining oil and 2 TBSP of butter. Add onions and cook for 2-3 minutes over medium high until softened. Add the mushrooms. Coat the mushrooms with the oil and butter and reduce heat to medium. The mushrooms will brown around the edges. Add garlic. Do not stir or move the mushrooms. Let them get crispy on the edges. After 3 minutes stir the entire mixture well and finish sautéing.
Add to the cooked mushrooms: the broth, Worcestershire sauce, wine and salt and pepper. Bring to a simmer.
Nestle the burgers into the sauce. Cover tightly, reduce heat to low and let simmer 15-17 minutes until burgers are cooked through. Add more broth or water if pan dries out too quickly. Remove the burgers, keep warm, add in final tablespoon of butter to the sauce.
Serve burgers with generous spoonfuls of sauce.