In a large pan over a low flame, heat 1/4 cup of the oil. Add the onions to the pan and cook for 45 to 60 minutes, stirring occasionally, until golden brown and fragrant. Remove from the heat and let cool.

Preheat the oven to 400 degrees Fahrenheit. Transfer the onions to a large bowl and mix with the remaining oil, salt, parsley, mushrooms, eggs and chicken broth.

In a separate small bowl, whisk the flour and baking powder. Stir it into the mushroom and onion mixture, reserving several mushrooms for topping, then season with black pepper.

Pour the kugel into a nine-inch round pie plate or pan greased with non-stick cooking spray. Top with the reserved mushrooms. Bake until golden, puffed and fragrant, around 50 minutes. Serve immediately.