In a skillet over medium heat, heat the oil and then cook the onions until translucent, about 5-8minutes. Turn the heat down to low, and cook, stirring occasionally, for 15 minutes more.
Add the mushrooms to the pan along with the pinch of sea salt and cook, stirring occasionally, until the mushrooms have released their juices and reduced in size.
Meanwhile, mix the burger ingredients together.
Form into 4-8 patties (depending on how thick/big you want them).
Heat a large cast-iron skillet or grill pan over medium-high heat on the stove or a grill to medium.
Cook the patties, turning once, until desired doneness, about 3-4 minutes a side for the smallerpatties, 5-6 minutes a side for the larger ones. Serve a scoopful of mushroom and onion mixture over the burger patties.