Wash the chanterelles and drain well. Cut the onion into wedges and the tomatoes into pieces. (Peeling tomatoes is optional.)
Heat 1 tablespoon oil in a pan over medium heat. Add the onion wedges and fry until softened, about 2–3 minutes. Add the chanterelles and tomatoes. Fry for 5–7 minutes over medium heat. Meanwhile, chop the parsley.
Season the mixture with salt, pepper, and nutmeg. Add white wine if desired. Simmer until the liquid has almost completely evaporated, about 3–5 minutes. Sprinkle the chopped parsley on top.