Heat oil in a large skillet or wok over medium heat. Add sliced potatoes and 2 tablespoons water. Cover and cook 10 minutes, stirring often.
Meanwhile, prepare cheese sauce. In a medium saucepan over medium-high heat, cook the onions in the butter until tender and translucent. Mix in the flour to form a paste.
Pour in half of the milk and whisk until well combined with a wire whisk. Add the rest of the milk and continue to stir until the mixture begins to bubble.
Remove from the heat and add the shredded cheese. Stir until the cheese is completely melted. At this point, add the butternut puree if desired. (see notes) Season with salt and pepper.
Stir in chicken and broccoli.
Add cheese sauce, milk and garlic powder. Heat to a gentle boil. Cover and cook over low heat 5 minutes more or until potatoes are tender. Sprinkle with parmesan cheese before serving.
Notes
I always have a ziplock bag of rotisserie chicken in my freezer for recipes like this. Find more on that here.I also grew a boat-load of butternut squash in my garden last year. I have baked and blended over 20 pounds of it into 2 cup portions. I freeze the puree in baggies and use it in soups and cheese sauces like this one. It adds a pop of vitamin A and a delicious nutty flavor to cheese sauce. I dare you to try it.