In a large skillet, heat 1 tablespoon of oil over low heat. Add sliced onions and cook until caramelized, stirring occasionally, about 40-60 minutes. Transfer to large bowl; set aside.
Heat remaining oil in skillet over medium-high heat. Add mushrooms and cook approximately 5 minutes, until mushrooms are softened and browned. Stir in kale and cook for 2 minutes.
Add sage, thyme, and broth to skillet. Bring to a simmer and cook for 5 minutes. Remove from heat.
Add bread and egg to caramelized onions; toss to combine. Stir in vegetable mixture and salt and pepper.
Pour stuffing into a large casserole dish coated with cooking spray or oil and cover. Bake for 30 minutes. Remove cover and spray top of stuffing with additional cooking spray. Bake for another 15-20 minutes or until golden brown.