Place a large, well-seasoned cast iron skillet over medium heat until it gets hot, about 5 minutes. Add sausage and cook until browned and no longer pink, about 5-7 minutes. Remove sausage and place in a bowl.
Leave grease (about 2 tablespoons worth) in the pan and add pumpkin. Cook for 10 minutes, stirring occasionally. Add onions and sauté for 5 minutes, stirring occasionally. Add mushrooms and cook for another 5 minutes. Finally add the kale and a little bit of water, cover, and let cook for 1-2 minutes until soft and wilted.
Add back in sausage along with the spices. Stir to combine and let sausage warm, about 2-3 minutes.