Gather and prep ingredients, and preheat the oven to 350°F (175°C). Grease a 9×13-inch casserole dish.
Heat oil and 1 Tbsp butter in a large skillet over medium heat. Add cubed chicken, ½ tsp salt, ¼ tsp pepper, and sear for 4-5 minutes until lightly golden (it doesn't need to be fully cooked), and transfer to a plate and set aside.
In the same skillet, melt 1 Tbsp butter and add sliced mushrooms, whites of green onions, and garlic, and cook for 6-8 minutes until softened and lightly browned.
Sprinkle flour over the vegetables and stir for 1-2 minutes to cook out the raw flour taste and form a roux.
Slowly whisk in chicken broth and milk. Simmer for 2-3 minutes until slightly thickened.
Stir in cottage cheese, sour cream, cheddar cheese, garlic powder, onion powder, and remaining ½ tsp salt and ¼ tsp pepper. Stir until melted and smooth.
Return the chicken to the skillet as well as the green parts of the onions. Stir until everything is coated.
Pour the chicken and mushroom mixture into your prepared casserole dish.
Crush the crackers in a zip-top bag using a rolling pin or similar tool. Toss with 1 Tbsp melted butter, then sprinkle evenly over the casserole.
Cover the casserole dish loosely with foil. Bake for 25 minutes. Remove foil and bake an additional 10-15 minutes until bubbly and golden.
Let it sit for 5-10 minutes before serving to allow the sauce to set slightly. Enjoy served sprinkled with extra green onion and over rice if desired.
*I always buy value packs of chicken breasts when I shop and individually freeze any I don't use right away. It keeps this recipe budget-friendly and makes weeknight cooking much easier, as I can just thaw what I need!**This recipe is tested and cost out using Better Than Bouillon. If using a different broth or stock, seasoning levels may vary. Taste before serving and adjust salt as needed.***Sharp cheddar gives the sauce a bolder, cheesier flavor without needing a ton of extra cheese. I recommend shredding it yourself if you can. Pre-shredded cheese is coated with anti-caking agents to prevent clumping and doesn't melt quite as smoothly into the sauce.****You can use any buttery cracker you like, such as Ritz or the grocery store brand, like the Great Value buttery rounds from Walmart.Make-Ahead Note: You can prepare the casserole filling and refrigerate it, covered, for up to 24 hours. Add the cracker topping right before baking. You may need to bake a few minutes longer if it's going into the oven cold!