Place the sweet onion and mushrooms in a food processor, and pulse until finely chopped. (You can chop these veggies by hand, but it is much easier to incorporate into the burgers if you use the food processor).
Put the ground turkey, onions and mushrooms, and spices in a mixing bowl. Use your hands to mix well.
Shape the burgers into patties that are about ½ inch thick. Depending on what you want to do, you can do 4 large patties, or 8 smaller patties, like sliders.
Place the oil in a skillet over medium heat. Gently set the patties in the skillet.
Cook over medium heat until the patties are done on the bottom - about 5 minutes, then flip. Continue to cook until they are browned on both sides and reach a temperature of 165 degrees F in the middle of the patties.
Serve warm in buns or toasted bread with the toppings of your choice.
Notes
Store leftover burgers in the refrigerator - they should stay fresh for 3-4 days.Nutrition facts are for patties only, not the buns or toppings.