Preheat the oven to 350. Have a large heavy skillet about 10-12 inches, for the potatoes and onions, and another large skillet for the mushrooms, since the mushrooms will contain a lot of water that needs to cook out.
Heat the chanterelles in a dry pan or with a touch of oil if it's not cast iron or non-stick, and cook slowly to brown gently and cook off their moisture.
Meanwhile, heat the other skillet with the oil and put the potatoes, cut side down into the pan. Cook the potatoes without moving them for 4-5 minutes, then put the onions, cut side down into the pan with them, If the pan looks dry, add a touch more oil. season the mixture to taste with salt and pepper, then put in the oven to cook through until the potatoes are just tender.
Remove the pan with the potatoes and onions from the oven, and if needed, put some extra color on them by cooking on the burner for a few more minutes. When the onions are nice and caramelized, carefully remove the top layer of onion skin, which can be stringy.
Add the hot mushrooms to the pan along with the garlic, reserved onion tops, parsley and the butter. Stir the mixture to combine, double check the seasoning for salt and pepper and serve immediately.
Notes
You can use other large mushrooms for this dish. Hen of the Woods or Maitake Mushrooms would be good, as would Saffron Milk Caps.